Geometry Homework

Question

A toy rocket is a composite of a cylindrical body with a cone for a nose. Find the volume of the rocket if the radius of the base is 1.25 inches, the height of the tip is 3 inches, and the height of the entire rocket is 15 inches.

A. 58.9 in^3

B. 176.6 in^3

C. 56.3 in^3

D. 63.8 in^3

Answer 1

Hey Leah,

This is a pretty straight forward 'plug and play' problem. All you need to do is find your formulas for the volume of a cone and the volume of a cylinder then plug in their respective values. Once you have the cylinder and the cone, add the two shapes together to make the whole rocket.

The formula for the volume of the cone is V = (pi)(r^2)h/3. You are given the radius (r = 1.25), and the height of the cone is the height of the tip (3 inches). Pi is of course 3.14 as it is usually rounded for geometry, but for more accuracy use the pi on your calculator while solving.

The formula for the volume of the cylinder is V = (pi)(r^2)h. For this part, you need the radius again because the cone and the cylinder share the same radius. The height however, is different here. If the entire rocket is 15 inches and we know the tip is 3 inches, then the cylindrical part of the rocket is 15-3 Inches, so 12 inches.

So plug in your values, then solve! When you add together the two shapes, you should get 63.82107782... in^3, or answer choice D when rounded.