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

I think it is B but if I’m wrong I’m very sorry...

The volume of a cubed shaped music box is 512 cubic

Thunderalesis7855

15.01.2022

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

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