A sphere is inscribed in a cylinder. Use complete sentences and geometric formulas to compare the surface area of the sphere and the lateral area of the cylinder.

(how do i explain this? also, correct answer will be marked brailnliest)

The word inscribed means that the sphere is inside the cylinder and its diameter is equal to the height and diameter of the cylinder. The surface area of the sphere is equal to

SA (sphere) = πd²

where d is the diameter.

That of the cylinder is,

SA (cylinder) = πd (h + d/2)

Since h is also equal to d

SA (cylinder) = πd (d + d/2) = 3πd²/2

Therefore, the surface area of the cylinder is approximately 1.5 times that of the sphere.