A right circular cylinder just encloses a sphere of radius 6 cm. If A and B are their curved surface areas, then:

Correct option is C

Given:

Radius of the sphere (r) = 6 cm
The cylinder just encloses the sphere, so the height of the cylinder (h) is equal to the diameter of the sphere.

Concept Used:
The curved surface area (CSA) of a sphere is given by the formula:
CSA of sphere =$$4 \pi r^2$$​​
The curved surface area (CSA) of a right circular cylinder is given by the formula:
CSA of cylinder = $$2 \pi r h$$​​
Since the height of the cylinder is equal to the diameter of the sphere, h = 2r.

Solution:
the CSA of the sphere.
CSA of sphere = $$4 \pi (6)^2 = 4 \pi \times 36 = 144 \pi \text{ cm}^2$$​

The CSA of the cylinder.
Since the height of the cylinder is twice the radius of the sphere, $$h = 2 \times 6 = 12 cm.$$​​
CSA of cylinder = $$2 \pi \times 6 \times 12 = 144 \pi \text{ cm}^2$$​​
The ratio of the curved surface areas.
The ratio of the curved surface area of the cylinder to the sphere is:
​$$\frac{CSA_{cylinder}}{CSA_{sphere}} = \frac{144 \pi}{144 \pi} = 1$$​​
The ratio of their curved surface areas is 1:1.

Then we can say A = B