The lateral surface area of the given cone A is exactly 1/2 the lateral surface area of cylinder B. Is it true or false?

Areas of various solids and shapes are one of the most fundamental topics in mathematics. They have plenty of applications in various fields.

Answer: It is true that the lateral surface area of the given cone A is exactly 1/2 the lateral surface area of cylinder B.

Let's understand the solution in detail.

Explanation:

From the above figure we can see that:

• The slant height of the cone = The height of the cylinder = h
• The radius of the cone = The radius of the cylinder = r

We know that the curved surface area or lateral surface area of the cylinder = 2π × (radius) × (height) = 2πrh

We also know that curved surface area or lateral surface area of the cone = π × (radius) × (slant height) = πrh

Therefore, the lateral surface area of the cylinder = 2 × (the lateral surface area of the cone)

or

The lateral surface area of the cone = 1/2 (the lateral surface area of the cylinder)

Check out more on the surface area of cylinder.

Hence, It is true that the lateral surface area of the given cone A is exactly 1/2 the lateral surface area of cylinder B.