Find the total surface area of a cube whose volume is 64 cm3 ?.
96 cm2
Cube Surface Area Calculation from Volume
To find the total surface area of a cube when its volume is known, we first determine the side length and then use it to calculate the surface area.
Side Length Determination
The volume ($V$) of a cube is calculated using the formula $V = a^3$, where '$a$' is the length of one side.
- Volume given: $V = 64 \text{ cm}^3$
- Set up the equation: $a^3 = 64 \text{ cm}^3$
- Solve for '$a$': $a = \sqrt[3]{64 \text{ cm}^3}$
- Result: $a = 4 \text{ cm}$
The side length of the cube is 4 cm.
Total Surface Area Calculation
The total surface area (TSA) of a cube is the sum of the areas of its six square faces. The formula is $TSA = 6a^2$.
- Substitute the side length $a = 4 \text{ cm}$: $TSA = 6 \times (4 \text{ cm})^2$
- Calculate the square of the side: $(4 \text{ cm})^2 = 16 \text{ cm}^2$
- Multiply by 6: $TSA = 6 \times 16 \text{ cm}^2 = 96 \text{ cm}^2$
The total surface area of the cube is $96 \text{ cm}^2$.
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