The ratio of the surface areas of two similar right cylinders is 25:16. What is the ratio of their volumes?

Question

The base of a triangle is 8 inches and the altitude is 17 inches. Find the area of the triangle.

 

The diameter of a cone measures 8 feet and the slant height is 9 feet. Find the surface area of the cone.

 

In a given trapezoid the bases have lengths 5 and 10 and a height of 3. Find the area of the trapezoid.

 

A sphere has a radius of 2. Find the volume.

 

What is the approximate volume of a can that is 5 inches tall and has a 2.5 inch diameter?

 

Answer 1

Area is proportional to the square of the cylinder's dimensions.  Volume is proportional to the cube.  If the ratio of the areas of the two cylinders is:

 

25:16 = 5²:4²

 

Then the ratio of the volumes will be 5³:4³ = 125:64