Question

The radius of a sphere is increased by 20%. What is the percentage increase in its volume?

• A. 72.8%
• B. 66.4%
• C. 48.8%
• D. 62.4%

Hint:

When a dimension of a 3D shape changes by \(x%\), the volume changes approximately by \((1+x/100)^3 - 1\) in decimal, multiply by 100 for percentage.

Answer 1

The Correct Option is A

Step 1: Let the original radius be \(r\).
Step 2: Volume of sphere is \[ V = \frac{4}{3} \pi r^3. \] Step 3: New radius = \[ r' = r + 0.20r = 1.2r. \] Step 4: New volume, \[ V' = \frac{4}{3} \pi (r')^3 = \frac{4}{3} \pi (1.2r)^3 = \frac{4}{3} \pi r^3 (1.2)^3 = V \times (1.728). \] Step 5: Percentage increase in volume, \[ \frac{V' - V}{V} \times 100 = (1.728 - 1) \times 100 = 0.728 \times 100 = 72.8%. \]