A cone has a volume of 130 cubic inches. What will be the volume of a cylinder with the same radius and height? Explain your reasoning.

Answer 1

The volume of a cylinder is pi(r²)h

Volume of a cone is 1/3 the volume of a cylinder of the same height

or (1/3)pi(r²)h

The cylinder has a volume 3 times that of a cone, if the height and radius are the same

3x130 = 390 cubic inches

If h=2r, if the height were double the radius, then the cylinder volume = the cone volume + a sphere volume if the radius is the same for all and the height is 2 times the radius. the cylinder volume =2pi(r)³ The cone is 1/3 of that or (2/3)pi(r)³ and the sphere is (4/3)pi(r)³ 2=2/3 + 4/3 = 6/3