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,

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

$a = \sqrt[3]{8 \times 8 \times 8}\\\\ a = \sqrt[3]{8^3}$

$a = (8^3)^{\frac{1}{3}}$

$a = 8$

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

$A = 6(8)^2\\\\A = 6 \times 64\\\\A = 384$

Thus surface area of music box is 384 square centimeter