Question

Assertion (A): A sphere is inscribed in a cylinder, the ratio of the volume of the cylinder to the volume of the sphere is 1 : 4.

Reason (R): Required ratio 4 = `πr^2 xx 2r : 4/3 πr^3`.

पर्याय

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

The volume of a cylinder enclosing a sphere of radius r is \[\pi r^2 \times (2r) = 2\pi r^3\], and the volume of the sphere is \[\frac{4}{3}\pi r^3\]. The ratio of the cylinder’s volume to the sphere’s volume is \[2\pi r^3 : \frac{4}{3}\pi r^3 = 2 : \frac{4}{3} = 3 : 2\] (or 3 : 4 inverted), which makes Assertion (A) stating the ratio is 1 : 4 false. However, Reason (R) correctly sets up the volume expressions, making it true.