Answer:<\/strong><\/h3>\n\n\n\nTo find the volume in deciliters (dL)<\/strong> of a piece of iron with mass 4.58 kg<\/strong> and density 7.86 g\/cm\u00b3<\/strong>, we first convert all units consistently to kg\/dL<\/strong> and then apply the density formula.<\/p>\n\n\n\n
\n\n\n\nStep 1: Convert density from g\/cm\u00b3 to kg\/dL<\/strong><\/h4>\n\n\n\nWe know:<\/p>\n\n\n\n
\n- 1 g = 0.001 kg<\/li>\n\n\n\n
- 1 cm\u00b3 = 1 mL<\/li>\n\n\n\n
- 100 mL = 1 dL<\/li>\n<\/ul>\n\n\n\n
So:Density=7.86 g\/cm3=7.86 g\/mL\\text{Density} = 7.86\\ \\text{g\/cm}^3 = 7.86\\ \\text{g\/mL}Density=7.86 g\/cm3=7.86 g\/mL<\/p>\n\n\n\n
Convert g\/mL to kg\/dL:7.86 g\/mL=0.00786 kg\/mL7.86\\ \\text{g\/mL} = 0.00786\\ \\text{kg\/mL}7.86 g\/mL=0.00786 kg\/mL0.00786 kg\/mL\u00d7100 mL\/dL=0.786 kg\/dL0.00786\\ \\text{kg\/mL} \\times 100\\ \\text{mL\/dL} = 0.786\\ \\text{kg\/dL}0.00786 kg\/mL\u00d7100 mL\/dL=0.786 kg\/dL<\/p>\n\n\n\n
\n\n\n\nStep 2: Use the formula for density<\/strong><\/h4>\n\n\n\nDensity=MassVolume\u21d2Volume=MassDensity\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}} \\Rightarrow \\text{Volume} = \\frac{\\text{Mass}}{\\text{Density}}Density=VolumeMass\u200b\u21d2Volume=DensityMass\u200bVolume=4.58 kg0.786 kg\/dL\u22485.83 dL\\text{Volume} = \\frac{4.58\\ \\text{kg}}{0.786\\ \\text{kg\/dL}} \\approx 5.83\\ \\text{dL}Volume=0.786 kg\/dL4.58 kg\u200b\u22485.83 dL<\/p>\n\n\n\n
\n\n\n\nFinal Answer:<\/strong><\/h3>\n\n\n\n5.83 dL\\boxed{5.83\\ \\text{dL}}5.83 dL\u200b<\/p>\n\n\n\n
\n\n\n\nExplanation:<\/strong><\/h3>\n\n\n\nTo solve this, understanding unit conversions is critical. The initial density is given in grams per cubic centimeter (g\/cm\u00b3)<\/strong>, which is equivalent to grams per milliliter (g\/mL)<\/strong> because 1 cm\u00b3 equals 1 mL. However, we are required to find volume in deciliters (dL)<\/strong> and the mass is given in kilograms (kg)<\/strong>. So, both the density and the mass need to be in compatible units.<\/p>\n\n\n\nWe convert grams to kilograms by dividing by 1000. Then we convert milliliters to deciliters by knowing that 100 mL equals 1 dL. By chaining these conversions, we rewrite the density in kg\/dL.<\/p>\n\n\n\n
Once the units match, we apply the formula for volume, which is mass divided by density. The final result gives the volume of the iron piece in deciliters. This process highlights how consistent units are essential when using formulas in science.<\/p>\n\n\n\n![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1090.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"Iron has a density of 7.86 g\/c m 3 ( 1 c m 3 =1 mL ). Calculate the volume (in dL ) of a piece of iron having a mass of 4.58 kg . Note that the density is provided in different units of volume and mass than the desired units of volume ( […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38917","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38917"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions"}],"predecessor-version":[{"id":38919,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions\/38919"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n
Step 1: Convert density from g\/cm\u00b3 to kg\/dL<\/strong><\/h4>\n\n\n\nWe know:<\/p>\n\n\n\n
\n- 1 g = 0.001 kg<\/li>\n\n\n\n
- 1 cm\u00b3 = 1 mL<\/li>\n\n\n\n
- 100 mL = 1 dL<\/li>\n<\/ul>\n\n\n\n
So:Density=7.86 g\/cm3=7.86 g\/mL\\text{Density} = 7.86\\ \\text{g\/cm}^3 = 7.86\\ \\text{g\/mL}Density=7.86 g\/cm3=7.86 g\/mL<\/p>\n\n\n\n
Convert g\/mL to kg\/dL:7.86 g\/mL=0.00786 kg\/mL7.86\\ \\text{g\/mL} = 0.00786\\ \\text{kg\/mL}7.86 g\/mL=0.00786 kg\/mL0.00786 kg\/mL\u00d7100 mL\/dL=0.786 kg\/dL0.00786\\ \\text{kg\/mL} \\times 100\\ \\text{mL\/dL} = 0.786\\ \\text{kg\/dL}0.00786 kg\/mL\u00d7100 mL\/dL=0.786 kg\/dL<\/p>\n\n\n\n
\n\n\n\nStep 2: Use the formula for density<\/strong><\/h4>\n\n\n\nDensity=MassVolume\u21d2Volume=MassDensity\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}} \\Rightarrow \\text{Volume} = \\frac{\\text{Mass}}{\\text{Density}}Density=VolumeMass\u200b\u21d2Volume=DensityMass\u200bVolume=4.58 kg0.786 kg\/dL\u22485.83 dL\\text{Volume} = \\frac{4.58\\ \\text{kg}}{0.786\\ \\text{kg\/dL}} \\approx 5.83\\ \\text{dL}Volume=0.786 kg\/dL4.58 kg\u200b\u22485.83 dL<\/p>\n\n\n\n
\n\n\n\nFinal Answer:<\/strong><\/h3>\n\n\n\n5.83 dL\\boxed{5.83\\ \\text{dL}}5.83 dL\u200b<\/p>\n\n\n\n
\n\n\n\nExplanation:<\/strong><\/h3>\n\n\n\nTo solve this, understanding unit conversions is critical. The initial density is given in grams per cubic centimeter (g\/cm\u00b3)<\/strong>, which is equivalent to grams per milliliter (g\/mL)<\/strong> because 1 cm\u00b3 equals 1 mL. However, we are required to find volume in deciliters (dL)<\/strong> and the mass is given in kilograms (kg)<\/strong>. So, both the density and the mass need to be in compatible units.<\/p>\n\n\n\nWe convert grams to kilograms by dividing by 1000. Then we convert milliliters to deciliters by knowing that 100 mL equals 1 dL. By chaining these conversions, we rewrite the density in kg\/dL.<\/p>\n\n\n\n
Once the units match, we apply the formula for volume, which is mass divided by density. The final result gives the volume of the iron piece in deciliters. This process highlights how consistent units are essential when using formulas in science.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Iron has a density of 7.86 g\/c m 3 ( 1 c m 3 =1 mL ). Calculate the volume (in dL ) of a piece of iron having a mass of 4.58 kg . Note that the density is provided in different units of volume and mass than the desired units of volume ( […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38917","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38917"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions"}],"predecessor-version":[{"id":38919,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions\/38919"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
So:Density=7.86 g\/cm3=7.86 g\/mL\\text{Density} = 7.86\\ \\text{g\/cm}^3 = 7.86\\ \\text{g\/mL}Density=7.86 g\/cm3=7.86 g\/mL<\/p>\n\n\n\n
Convert g\/mL to kg\/dL:7.86 g\/mL=0.00786 kg\/mL7.86\\ \\text{g\/mL} = 0.00786\\ \\text{kg\/mL}7.86 g\/mL=0.00786 kg\/mL0.00786 kg\/mL\u00d7100 mL\/dL=0.786 kg\/dL0.00786\\ \\text{kg\/mL} \\times 100\\ \\text{mL\/dL} = 0.786\\ \\text{kg\/dL}0.00786 kg\/mL\u00d7100 mL\/dL=0.786 kg\/dL<\/p>\n\n\n\n
\n\n\n\n
Step 2: Use the formula for density<\/strong><\/h4>\n\n\n\nDensity=MassVolume\u21d2Volume=MassDensity\\text{Density} = \\frac{\\text{Mass}}{\\text{Volume}} \\Rightarrow \\text{Volume} = \\frac{\\text{Mass}}{\\text{Density}}Density=VolumeMass\u200b\u21d2Volume=DensityMass\u200bVolume=4.58 kg0.786 kg\/dL\u22485.83 dL\\text{Volume} = \\frac{4.58\\ \\text{kg}}{0.786\\ \\text{kg\/dL}} \\approx 5.83\\ \\text{dL}Volume=0.786 kg\/dL4.58 kg\u200b\u22485.83 dL<\/p>\n\n\n\n
\n\n\n\nFinal Answer:<\/strong><\/h3>\n\n\n\n5.83 dL\\boxed{5.83\\ \\text{dL}}5.83 dL\u200b<\/p>\n\n\n\n
\n\n\n\nExplanation:<\/strong><\/h3>\n\n\n\nTo solve this, understanding unit conversions is critical. The initial density is given in grams per cubic centimeter (g\/cm\u00b3)<\/strong>, which is equivalent to grams per milliliter (g\/mL)<\/strong> because 1 cm\u00b3 equals 1 mL. However, we are required to find volume in deciliters (dL)<\/strong> and the mass is given in kilograms (kg)<\/strong>. So, both the density and the mass need to be in compatible units.<\/p>\n\n\n\nWe convert grams to kilograms by dividing by 1000. Then we convert milliliters to deciliters by knowing that 100 mL equals 1 dL. By chaining these conversions, we rewrite the density in kg\/dL.<\/p>\n\n\n\n
Once the units match, we apply the formula for volume, which is mass divided by density. The final result gives the volume of the iron piece in deciliters. This process highlights how consistent units are essential when using formulas in science.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Iron has a density of 7.86 g\/c m 3 ( 1 c m 3 =1 mL ). Calculate the volume (in dL ) of a piece of iron having a mass of 4.58 kg . Note that the density is provided in different units of volume and mass than the desired units of volume ( […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38917","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38917"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions"}],"predecessor-version":[{"id":38919,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions\/38919"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
5.83 dL\\boxed{5.83\\ \\text{dL}}5.83 dL\u200b<\/p>\n\n\n\n
\n\n\n\n
Explanation:<\/strong><\/h3>\n\n\n\nTo solve this, understanding unit conversions is critical. The initial density is given in grams per cubic centimeter (g\/cm\u00b3)<\/strong>, which is equivalent to grams per milliliter (g\/mL)<\/strong> because 1 cm\u00b3 equals 1 mL. However, we are required to find volume in deciliters (dL)<\/strong> and the mass is given in kilograms (kg)<\/strong>. So, both the density and the mass need to be in compatible units.<\/p>\n\n\n\nWe convert grams to kilograms by dividing by 1000. Then we convert milliliters to deciliters by knowing that 100 mL equals 1 dL. By chaining these conversions, we rewrite the density in kg\/dL.<\/p>\n\n\n\n
Once the units match, we apply the formula for volume, which is mass divided by density. The final result gives the volume of the iron piece in deciliters. This process highlights how consistent units are essential when using formulas in science.<\/p>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"Iron has a density of 7.86 g\/c m 3 ( 1 c m 3 =1 mL ). Calculate the volume (in dL ) of a piece of iron having a mass of 4.58 kg . Note that the density is provided in different units of volume and mass than the desired units of volume ( […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38917","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38917"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions"}],"predecessor-version":[{"id":38919,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions\/38919"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
We convert grams to kilograms by dividing by 1000. Then we convert milliliters to deciliters by knowing that 100 mL equals 1 dL. By chaining these conversions, we rewrite the density in kg\/dL.<\/p>\n\n\n\n
Once the units match, we apply the formula for volume, which is mass divided by density. The final result gives the volume of the iron piece in deciliters. This process highlights how consistent units are essential when using formulas in science.<\/p>\n\n\n\n Iron has a density of 7.86 g\/c m 3 ( 1 c m 3 =1 mL ). Calculate the volume (in dL ) of a piece of iron having a mass of 4.58 kg . Note that the density is provided in different units of volume and mass than the desired units of volume ( […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-38917","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=38917"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions"}],"predecessor-version":[{"id":38919,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/38917\/revisions\/38919"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=38917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=38917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=38917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}<\/figure>\n","protected":false},"excerpt":{"rendered":"