Consider the following statements about spheres:
I. The surface area of a sphere of radius 5 cm is \(100\pi\) cm2.
II. If the radius of a sphere is doubled, its volume becomes 4 times the original volume.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Only I
For a sphere of radius \(r\): surface area \(=4\pi r^2\) and volume \(=\frac{4}{3}\pi r^3\). The volume depends on the cube of the radius.
Statement I — Correct.
Surface area \(=4\pi\times5^2=4\pi\times25=100\pi\) cm2
Statement II — Incorrect.
New volume \(=\frac{4}{3}\pi(2r)^3=8\times\frac{4}{3}\pi r^3\)
The volume becomes 8 times, not 4 times (4 times is what happens to the surface area).
Only statement I is correct.