The volume of the solid in cubic?

Question

The base of a solid is a circle of radius 2 inches. Each cross section perpendicular to a certain diameter is a square with one side lying in the circle. The volume of the solid in cubic inches is 

 

a) 16

b) 16pi

c) 128/3

d) 128pi/3

e) 32pi

 

Answer: C

 

Please show all your work. 

Answer 1

The solid has to be a cylinder with the circle as a base.

 

V_cyl = B h; where B is the area of the Base.

 

B = pi r^2 = pi 2^2 = 4 pi square inches

 

"Each cross section perpendicular to a certain diameter is a square."

 

So h = diameter of circle = 2 r = 2*2 = 4 inches

 

V_cyl = 4 pi h = 4 pi 4 = 16 pi cubic inches

 

Answer is B, not C.