Question

The volume of a cubed shaped music box is 512 cubic centimeters find the surface area of the music box

Answer 1

The surface area of music box is 384 square centimeter

Solution:

Given that,

Volume of cubed shaped music box = 512 cubic centimeter

To find: Surface area of music box

The volume of cube is given as:

`volume = a^3`

Where, "a" is the length of side

Therefore,

`512 = a^3`

Taking cube root on both sides,

`a = \sqrt[3]{512}`

`a = \sqrt[3]{8 * 8 * 8}\\\\ a = \sqrt[3]{8^3}`

`a = (8^3)^{(1)/(3)}`

`a = 8`

Thus length of side of cube is 8 cm

Find surface area of cubed shaped music box

The surface area of cube is given as:

`A = 6a^2`

Substitute a = 8 in above formula

`A = 6(8)^2\\\\A = 6 * 64\\\\A = 384`

Thus surface area of music box is 384 square centimeter