How many pencil boxes of dimensions 15cm x 5cm x 2cm can be packed in a carton, each of whose edges is 30cm?<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n To find how many pencil boxes can be packed into a carton, we need to compare the volume of the carton to the volume of one pencil box, and also consider how they can be arranged inside the carton.<\/p>\n\n\n\n Each pencil box has dimensions:<\/p>\n\n\n\n So, the volume<\/strong> of one pencil box is: 15\u00d75\u00d72=150 cm315 \\times 5 \\times 2 = 150 \\text{ cm}^3<\/p>\n\n\n\n Each edge of the carton is 30 cm. This makes it a cube: 30\u00d730\u00d730=27,000 cm330 \\times 30 \\times 30 = 27,000 \\text{ cm}^3<\/p>\n\n\n\n 27000150=180\\frac{27000}{150} = 180<\/p>\n\n\n\n So theoretically<\/strong>, 180 boxes can fit<\/strong> based on volume alone.<\/p>\n\n\n\n Let\u2019s check how many boxes can fit along each dimension<\/strong> of the carton:<\/p>\n\n\n\n So, by placing boxes 15 cm \u00d7 5 cm \u00d7 2 cm<\/strong> in a 30 cm \u00d7 30 cm \u00d7 30 cm<\/strong> carton:<\/p>\n\n\n\n Now multiply: 2\u00d76\u00d715=1802 \\times 6 \\times 15 = 180<\/p>\n\n\n\n To determine how many pencil boxes can be packed into a cube-shaped carton, we consider both volume and physical arrangement. Each pencil box measures 15 cm long, 5 cm wide, and 2 cm high. The carton has a cubic shape, each edge being 30 cm long. First, calculate the volume of one pencil box: 15\u00d75\u00d72=150 cm315 \\times 5 \\times 2 = 150 \\text{ cm}^3<\/p>\n\n\n\n Next, calculate the volume of the carton: 30\u00d730\u00d730=27,000 cm330 \\times 30 \\times 30 = 27,000 \\text{ cm}^3<\/p>\n\n\n\n Now, dividing the total volume of the carton by the volume of one pencil box: 27,000\u00f7150=18027,000 \\div 150 = 180<\/p>\n\n\n\n This gives a theoretical maximum of 180 boxes, assuming perfect packing. However, we must ensure the boxes can actually fit<\/strong> inside the carton in terms of orientation and dimensions<\/strong>. We evaluate how many boxes can fit along each axis of the carton:<\/p>\n\n\n\n This configuration gives: 2\u00d76\u00d715=180 boxes2 \\times 6 \\times 15 = 180 \\text{ boxes}<\/p>\n\n\n\n This confirms that not only do the boxes fit in terms of volume, but they also fit exactly with no wasted space, provided they are aligned correctly. Therefore, the carton can hold exactly 180 pencil boxes<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" How many pencil boxes of dimensions 15cm x 5cm x 2cm can be packed in a carton, each of whose edges is 30cm? The correct answer and explanation is: To find how many pencil boxes can be packed into a carton, we need to compare the volume of the carton to the volume of one […]<\/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-17148","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17148","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=17148"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17148\/revisions"}],"predecessor-version":[{"id":17150,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/17148\/revisions\/17150"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=17148"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=17148"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=17148"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep 1: Volume of the pencil box<\/strong><\/h3>\n\n\n\n
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\n\n\n\nStep 2: Volume of the carton<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 3: Theoretical number of boxes (volume-wise)<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 4: Check for actual fit by arrangement<\/strong><\/h3>\n\n\n\n
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\n\n\n\n\u2705 Final Answer: 180 pencil boxes<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300 words)<\/strong><\/h3>\n\n\n\n
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