A closed box has a square base with side length l feet and height h feet. Given that the volume of the box is 35 cubic feet, express the surface area of the box in terms of l only. ??

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A closed box has a square base with side length l feet and height h feet. Given that the volume of the box is 35 cubic feet, express the surface area of the box in terms of l only. ??

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Answer 1 · 2017-08-23T22:55:22

$A = \frac{2 (70 + I^{3})}{I}$ $A = (2(70+I^3))/I$

Explanation:

So we are told that the box has a square base, so all four sides are the same length I.

Volume = Length x Breadth x Height

So we know that Length and Breadth are both equal to I. Hence

$35 = I \cdot I \cdot h$ $35 = I*I*h$

$\Rightarrow h = \frac{35}{I^{2}}$ $implies h = 35/I^2$

Now we need to calculate the surface are of the box. There are four side faces with area $I \cdot h$ $I*h$ as well as a top and bottom face of area $I^{2}$ $I^2$ . Therefore

$A = 4 (I \cdot h) + 2 I^{2}$ $A = 4(I*h) + 2I^2$

$A = 4 I \cdot \frac{35}{I^{2}} + 2 I^{2}$ $A = 4I*35/I^2 + 2I^2$

$A = \frac{140}{I} + 2 I^{2}$ $A = 140/I + 2I^2$

$A = \frac{2 (70 + I^{3})}{I}$ $A = (2(70+I^3))/I$

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A closed box has a square base with side length l feet and height h feet. Given that the volume of the box is 35 cubic feet, express the surface area of the box in terms of l only. ??

1 Answer

Explanation:

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