The amount of ice on Marspolar caps is 2 km thick and has a radius of 400 km (the area of a circle is ), then the amount of water on Mars is 2.54 1015 tons. 3.21 x 1014 tons<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Let’s analyze the problem step-by-step:<\/p>\n\n\n\n Given:<\/strong><\/p>\n\n\n\n The ice layer is roughly a cylinder (ice thickness \u00d7 area): Volume=Area\u00d7Thickness\\text{Volume} = \\text{Area} \\times \\text{Thickness}<\/p>\n\n\n\n Calculate the area: A=\u03c0r2=\u03c0\u00d7(400 km)2=\u03c0\u00d7160000=502,654 km2A = \\pi r^2 = \\pi \\times (400 \\text{ km})^2 = \\pi \\times 160000 = 502,654 \\text{ km}^2<\/p>\n\n\n\n Now multiply by thickness (2 km): V=502,654 km2\u00d72 km=1,005,308 km3V = 502,654 \\text{ km}^2 \\times 2 \\text{ km} = 1,005,308 \\text{ km}^3<\/p>\n\n\n\n We need the density of ice to convert volume to mass. First, convert volume from km\u00b3 to m\u00b3: 1 km3=(1000 m)3=109 m31 \\text{ km}^3 = (1000 \\text{ m})^3 = 10^9 \\text{ m}^3 V=1,005,308 km3=1,005,308\u00d7109=1.0053\u00d71015 m3V = 1,005,308 \\text{ km}^3 = 1,005,308 \\times 10^9 = 1.0053 \\times 10^{15} \\text{ m}^3<\/p>\n\n\n\n Mass in kilograms: m=density\u00d7volume=917 kg\/m3\u00d71.0053\u00d71015 m3=9.22\u00d71017 kgm = \\text{density} \\times \\text{volume} = 917 \\text{ kg\/m}^3 \\times 1.0053 \\times 10^{15} \\text{ m}^3 = 9.22 \\times 10^{17} \\text{ kg}<\/p>\n\n\n\n Convert kilograms to tons (1 ton = 1000 kg): m=9.22\u00d710171000=9.22\u00d71014 tonsm = \\frac{9.22 \\times 10^{17}}{1000} = 9.22 \\times 10^{14} \\text{ tons}<\/p>\n\n\n\n Our result is between the two options, closer to 10\u00b9\u2075 than 10\u00b9\u2074 but not exactly 2.54 \u00d7 10\u00b9\u2075.<\/p>\n\n\n\n Based on calculations, the amount of water ice on Mars polar caps is approximately 9.2 \u00d7 10\u00b9\u2074 tons<\/strong>. Among the two choices, 3.21 \u00d7 10\u00b9\u2074 tons<\/strong> is closer to this value than 2.54 \u00d7 10\u00b9\u2075 tons, so 3.21 \u00d7 10\u00b9\u2074 tons is the more reasonable estimate<\/strong>.<\/p>\n\n\n\n The problem asks to estimate the amount of water ice on Mars’ polar caps given the ice thickness and radius of the ice-covered area. First, we calculate the surface area of the polar caps using the formula for the area of a circle A=\u03c0r2A = \\pi r^2. With a radius of 400 km, the area is about 502,654 km\u00b2. Multiplying this by the thickness of the ice (2 km), we find the volume of ice to be roughly 1,005,308 km\u00b3.<\/p>\n\n\n\n To find the mass, we convert volume to cubic meters and then multiply by the density of ice (approximately 917 kg\/m\u00b3). This yields a mass of about 9.22 \u00d7 10\u00b9\u2077 kg, or 9.22 \u00d7 10\u00b9\u2074 tons after converting kilograms to tons.<\/p>\n\n\n\n Comparing this value to the provided options (2.54 \u00d7 10\u00b9\u2075 tons and 3.21 \u00d7 10\u00b9\u2074 tons), our estimate falls closer to the lower one, 3.21 \u00d7 10\u00b9\u2074 tons. Differences could arise from variations in ice density, actual thickness, or radius estimates.<\/p>\n\n\n\n Therefore, the best choice for the total amount of water on Mars’ polar caps is approximately 3.21 \u00d7 10\u00b9\u2074 tons<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" The amount of ice on Marspolar caps is 2 km thick and has a radius of 400 km (the area of a circle is ), then the amount of water on Mars is 2.54 1015 tons. 3.21 x 1014 tons The correct answer and explanation is: Let’s analyze the problem step-by-step: Given: Step 1: Calculate […]<\/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-19926","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19926","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=19926"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19926\/revisions"}],"predecessor-version":[{"id":19927,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/19926\/revisions\/19927"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=19926"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=19926"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=19926"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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\n\n\n\nStep 1: Calculate the volume of ice<\/h3>\n\n\n\n
\n\n\n\nStep 2: Convert volume to mass (tons)<\/h3>\n\n\n\n
Density of ice \u2248 0.917 g\/cm\u00b3 = 917 kg\/m\u00b3<\/p>\n\n\n\n
\n\n\n\nStep 3: Compare with given options<\/h3>\n\n\n\n
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\n\n\n\nPossible reason for discrepancy:<\/h3>\n\n\n\n
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\n\n\n\nConclusion:<\/h3>\n\n\n\n
\n\n\n\nExplanation Summary (300 words):<\/h3>\n\n\n\n