Question

Find the volume of a cube whose surface area is 96 cm³.

• A. 27 cm³
• B. 64 cm³
• C. 8 cm³
• D. 1 cm³

Answer 1

Answer:

B. 64 cm³

Surface Area of a Cube

• The total surface area (TSA) of a cube is the sum of the areas of its six square faces.

• Since each face is a square with side length 'a', the area of one face is a².

• As there are six such faces, the formula for the total surface area of a cube is TSA = 6a².

• In the given problem, the surface area is 96 cm³. We use this to find the side length.

• Setting up the equation: 6a² = 96 cm².

• Dividing both sides by 6: a² = 16 cm².

• Taking the square root: a = √16 cm = 4 cm.

• Therefore, the side length of the cube is 4 cm.

Volume of a Cube

• The volume (V) of a cube is the amount of space it occupies.

• It is calculated by multiplying the length, width, and height. Since all are equal to 'a' in a cube, the formula is V = a × a × a = a³.

• Using the side length calculated (a = 4 cm):

• Volume V = (4 cm)³.

• Volume V = 4 × 4 × 4 cm³.

• Volume V = 64 cm³.

• This is the final volume of the cube.