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Apply solids across unfamiliar problems: original cases with explanations after your first response.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
Separate boundary area from enclosed volume and keep all length units consistent. A cross-section, a space diagonal and a surface face may require different models of the same solid.
A rectangular box has dimensions 3,4 and 12. What is the length of its space diagonal?
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A cylinder has radius 3 and height 8. What is its volume divided by pi?
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A cube has total surface area 150. What is its volume?
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A rectangular tank is 50 cm long and 30 cm wide. Adding 6 liters of water raises the depth by how many centimeters? One liter is 1000 cubic centimeters.
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Every edge of a solid model is multiplied by 1.5. By what factor does its volume change?
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A closed box has length 8, width 5 and height 3. What is its total surface area?
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A cylinder's radius is halved and its height is doubled. What fraction of the original volume remains? Enter a decimal.
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A rectangular prism has volume 144 and a square base with perimeter 24. What is its height?
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An open rectangular container has base 10 by 6 and height 4. What is the area of its base and four sides, excluding the open top?
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Two cubes of edges 3 and 6 are melted without loss into nine identical smaller cubes. What is the edge of each smaller cube?
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Verify the dimensional power in each scale change; if a formula is supplied, map its symbols to the actual perpendicular height and base.