Question

box with a a square base and open top must have a volume of 62,500 cm3. Find the dimensions of the box that minimize the amount of material used. sides of base

Answer 1

Answer:

The dimensions of the box that minimize the amount of material used is

39.69 cm

Step-by-step explanation:

This problem is on the mensuration of solids, a box

we know that the volume of a box is give by the expression

$Volume= L^3$

now to find the dimension of the box, we need to find L

Given data

volume = $62,500 cm^3$.

$62,500 cm^3= L^3\\L=\sqrt[3]{62500} \\\L=39.69 cm$

Answer 2

Answer:

The dimensions of box that will minimize the amount of material used is $39.69cm$

Step-by-step explanation:

Given information

Volume $V=62500cm^3$

As given in question the box is of square shape:

So the volume will be

$V=L^3$

where, L is the side of the square

$V=L^3=62500\\L=\sqrt[3]{62500} \\L=39.69 cm$

Hence, The dimensions of box that will minimize the amount of material used is $39.69cm$.

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