If each side of a cube is reduced by 50%, the surface area will reduced by. Option 1: 75% Option 2: 50% Option 3: 25% Option 4: 100%

Answer: 75%. Solution: Original surface area of cube with side a is 6a^2. New side is a/2, so new surface area is 6 x (a/2)^2 = 6a^2/4 = 3a^2/2. Reduction = 6a^2 - 3a^2/2 = 9a^2/2. Percentage reduction = (9a^2/2)/6a^2 x 100 = 75%.

Geometry

Solids

Easy

If each side of a cube is reduced by 50%, the surface area will reduced by.

75%

50%

25%

100%

✅ Correct Option: 1

Original surface area of cube with side $a$ is $6a^2$ . New side is $\frac{a}{2}$ , so new surface area is $6 \times (\frac{a}{2})^2 = \frac{6a^2}{4} = \frac{3a^2}{2}$ .

Reduction $= 6a^2 - \frac{3a^2}{2} = \frac{9a^2}{2}$ .

Percentage reduction $= \frac{9a^2/2}{6a^2} \times 100 = 75\%$ .

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Solution

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