The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B. True or false.

Cones and cylinders are very important solids with many different applications. Let's talk about their curved or lateral surface areas in this section.

Answer: Yes, it is true that the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.

Let's understand why.

Explanation: 

From the given figure, we see that:

• The slant height of the cone = Two times the height of the cylinder = 2h
• The radius of the cone = The radius of the cylinder = r

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

We also know that lateral surface area of the cone = π × (radius) × (slant height) = πr(2h) = 2πrh.

Therefore, the lateral surface area of the cylinder = the lateral surface area of the cone.

Check out more information on the surface area of a cylinder.

Hence, it is true that the lateral surface area of the given cone A is exactly equal to the lateral surface area of cylinder B.