Grade 8 · Math

8th grade Volume of cones and spheres worksheet

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Volume of cones and spheres

Grade 8 Math Worksheet - Challenge Me

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Luz fills a can with a cone of water. The cone: radius 3 cm, height 6 cm. The can: radius 6 cm, height 6 cm. How many full cones of water fill the can?
Noah fills a can with a cone of water. The cone: radius 3 cm, height 12 cm. The can: radius 12 cm, height 15 cm. How many full cones of water fill the can?
Pia's ball (radius 4.5 cm) fits snugly in a can as tall as it is wide. How many cubic cm of air surround it? Use π = 3.14. Do not round.
Ari's castle tower: a cylinder tower (radius 4 cm, height 9 cm) with a cone roof (same radius, height 6 cm) on top. What is its volume in cubic cm? Use π = 3.14.
Bo's new pencil: a cylinder body (radius 0.5 cm, height 15 cm) with a cone tip (same radius, height 3 cm) on top. What is its volume in cubic cm? Use π = 3.14.
Use the picture in question 4.
Esme's castle roof is a cone with a volume of 307.72 cubic cm and a height of 6 cm. What is its radius, in cm? Use π = 3.14.
Jun's toy volcano is a cone with a volume of 75.36 cubic cm and a height of 8 cm. What is its radius, in cm? Use π = 3.14.
Luz has two balls. The second ball's radius is 2 times as long as the first one's. How many times as much does the second ball hold?
Milo has two balls. The second ball's radius is 3 times as long as the first one's. How many times as much does the second ball hold?
Pia has two castle roofs with the same height. The second one's radius is 5 times as long as the first one's. How many times as much does the second hold?

8th grade Volume of cones and spheres worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Volume of cones and spheres. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the volume of a cone: one third of the cylinder with the same base and height.
I can find the volume of a ball (sphere): two thirds of the snug cylinder around it, which is 4/3 × 3.14 × r × r × r.
I can work back to a cone's height or radius, add the volumes of a cone and a cylinder, and say how the volume changes when the radius changes.

Standard: 8.G.C.9 (cones, spheres)

Words to know

cone: A solid with a flat circle at the bottom and a point at the top.

sphere: A solid like a ball: every point on it is the same distance from the middle.

radius: The distance from the middle to the edge of the circle, or to the surface of a sphere.

diameter: The distance all the way across through the middle: twice the radius.

snug: Touching all the way round, with no room to spare, like a ball in a can as tall as it is wide.

cubic units: The units for volume, like cubic cm.

Common mistakes

Your child added the height to the area of the base instead of multiplying.

Your child gave the volume of the cylinder instead of the cone or the ball.

Your child used one half where a cone needs one third (or a ball two thirds).

What to say

Ask: if one layer holds 10 and there are 5 layers, how much is that in all?

Ask: does a cone fill the whole can? How many cones fill it?

Ask: how many cones fill the can? Is that two or three?

Questions parents ask

What is the most common mistake with volume of cones and spheres?

Your child added the height to the area of the base instead of multiplying.

How can I help my child with volume of cones and spheres?

Ask: if one layer holds 10 and there are 5 layers, how much is that in all?

Are these 8th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 8 math

See all grade 8 math

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