Volume of cones, Cylinders and Spheres Worksheets, Grade 8 (8.G.C.9) – Free PDF + Answer Key

First page of the volume of cones, cylinders and spheres practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

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Key idea

Cylinder πr²h; cone ⅓πr²h; sphere ⁴⁄₃πr³. Cone = a third of its cylinder; sphere = two thirds of its containing cylinder. Halve every diameter first: r is squared or cubed, so a diameter used as a radius costs a factor of 4 or 8.

Sample problems

Write the three volume formulas.
A cylinder has radius 3 and height 10. Find its volume as a multiple of π.
Find the volume of a cone with radius 3 and height 10. Use your answer to item 2.
Find the volume of a sphere of radius 3.

Common mistakes to watch for

Used 8 as the radius, giving 640π — which is item 3. Halving the diameter is the first line, not a detail.
Gave 160π, dropping the third. Three times too big, and an answer three times too big looks perfectly reasonable, which is why it survives.
Said he “used the wrong number”. The question asks how the SIZE of the error shows it — exactly 4 times is the diagnosis, and an arithmetic slip would not land on a whole-number factor.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.