Multiple choice

A right circular cylinder just encloses a sphere. If p is the surface area of the sphere and q is the curved surface area of the cylinder, then which one of the following is correct?

  1. p = q

  2. p = 2q

  3. 2p = q

  4. 2p = 3q
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sphere radius r, cylinder radius r, height 2r. Surface area of sphere p = 4*pi*r^2. Curved surface area of cylinder q = 2*pi*r*h = 2*pi*r*(2r) = 4*pi*r^2. Thus p = q.

AI explanation

Let the radius of the enclosed sphere be r. When a right circular cylinder just encloses this sphere, the height of the cylinder equals the diameter of the sphere, so h = 2r, and the radius of the cylinder equals r. The surface area of the sphere is found by the formula 4 * pi * r^2. The curved surface area of the cylinder is found by the formula 2 * pi * r * h, and substituting h with 2r gives 2 * pi * r * 2r = 4 * pi * r^2. Therefore, the surface area of the sphere equals the curved surface area of the cylinder, meaning p = q.

Keep practicing — related questions