Figure a is a cylinder. figure b is a cone. the figures have the same height and the circular bases have the same diameter. which statement is true? a) the volume of a is 2 times the volume of b b) the volume of the cone is equal to the volume of the cylinder. c) the base of the cone and the top of the cylinder have the same area. d) the surface area of the cylinder and the surface area of the cone are equal.

C)The base of the cone and the top of the cylinder have the same area.

Step-by-step explanation:

Given : Cylinder and Cone with same height and radius .

Solution :

Since height and radius is same of both cone and cylinder.

Volume of cone is

Volume of cylinder is  

Thus the volume of cone is 1/3 rd the volume of cylinder having same radius and height.

Thus Option A and B is wrong

Option C )The base of the cone and the top of the cylinder have the same area.

Since radius is same

Base of cone =

Base of cylinder =  

refer attached file .

Thus Option C is correct

Option D : The surface area of the cylinder and the surface area of the cone are equal.

Since height an radius is same

Thus the surface area of cone is

Surface area of cylinder is

Thus areas are not equal

Hence Option D is wrong .