Question

The manufacturer of a gift box designs a box with length and width each twice as long as its height. Find a formula that gives the height h of the box in terms of its volume V. Then give the length of the box if the volume is 640 cm 3 .

Answer 1

Volume = 4H^3, and

Length = 10.86 cm

Explanation:

The volume of a box is given by:

Volume = W*L*H,

where W, L, and H are the Width, Length, and Height of the box.

We are told that both the length, L, and the width, W are twice as long as the height:

L = 2H, and

W = 2H

Take the first equation and substitute these two expression for L and w:

Volume = W*L*H

Volume = (2H)*(2H)*H

Volume = 4H^3

We know the volume, so we can say:

640 cm^3 = 4H^3

4H^3 = 640 cm^3

H^3 = 160

H = 5.43 cm

L = 2H

L = 10.86 cm