A cube has a total surface area of 384 cm^2. What is the volume of the cube? Option 1: 512 cm^3 Option 2: 576 cm^3 Option 3: 648 cm^3 Option 4: 729 cm^3

Answer: 512 cm^3. Solution: For a cube of edge a, surface area = 6a^2. 6a^2 = 384 a^2 = 64 a = 8 cm. Volume = a^3 = 8^3 = 512 cm^3.

Geometry

Solids

Easy

A cube has a total surface area of 384 $cm^2$ . What is the volume of the cube?

512 $cm^3$

576 $cm^3$

648 $cm^3$

729 $cm^3$

✅ Correct Option: 1

For a cube of edge $a$ , surface area $= 6a^2$ .

$6a^2 = 384 \Rightarrow a^2 = 64 \Rightarrow a = 8$ cm.

Volume $= a^3 = 8^3 = 512$ cm $^3$ .

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A cube has a total surface area of 384 $cm^2$ . What is the volume of the cube?