Question

The radius of the sphere is increased by 100% then the volume of the resultant sphere is increased by

• A. 200%
• B. 700%
• C. 500%
• D. 900%

Answer 1

The Correct Option is B

To solve the problem, we need to determine how much the volume of a sphere increases when its radius is increased by 100%.

1. Original Volume of the Sphere:
The volume of a sphere is given by:

$ V = \frac{4}{3} \pi r^3 $

2. New Radius After 100% Increase:

100% increase in radius means the new radius becomes:

$ r' = r + 1.0r = 2r $

3. New Volume of the Sphere:

$ V' = \frac{4}{3} \pi (2r)^3 = \frac{4}{3} \pi \cdot 8r^3 = 8 \cdot \left(\frac{4}{3} \pi r^3\right) = 8V $

4. Percentage Increase in Volume:

Increase = $ V' - V = 8V - V = 7V $

Percentage increase = $ \frac{7V}{V} \times 100 = 700\% $

Final Answer:
The volume is increased by $ {700\%} $.