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What are the dimensions of a 18cm3 rectangular prism with the smallest surface area?
Ambao123
Let's call the sides a, b, c. The rectangular prism with the smallest surface area is a cube.
If the volume is 18cm^3 (18 cubic cm), then a x b x c=18. But since it's a cube, the sides are the same size. So the formula for volume is a^3=18 (i.e. a cubed = 18)
Then each side of the cube will be the cube root of 18 (which is 2.62074139 to 8 decimal places)
So the dimensions of the rectangular prism rounded to 2dp are 2.62 x 2.62 x 2.62.
And the surface area using the rounded values is 41.19 to 2DP
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∙ 8y ago
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