Grades Grade 8 GeometryVolume of Cylinders, Cones & Spheres

Volume of Cylinders, Cones & Spheres

📐 Geometry

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Volume of Cylinders, Cones & Spheres

Three key volume formulas — one for each curved solid — all built around π and the radius.

The volumes of cylinders, cones, and spheres all involve π and the radius r. Notice that a cone's volume is exactly one-third of the cylinder with the same base and height — a powerful relationship to remember.

V_{\text{cylinder}} = \pi r^2 h

V_{\text{cone}} = \frac{1}{3}\pi r^2 h

V_{\text{sphere}} = \frac{4}{3}\pi r^3

🥫Soup can (cylinder)

A can has radius 3 cm and height 10 cm.

V = π(3²)(10) = 90π ≈ 282.7 cm³

V = \pi(3)^2(10) = 90\pi \approx 282.7 \text{ cm}^3

🏀Basketball (sphere)

A basketball has radius 12 cm.

V = (4/3)π(12³) = (4/3)π(1728) = 2304π ≈ 7238.2 cm³

V = \frac{4}{3}\pi(12)^3 = \frac{4}{3}\pi(1728) = 2304\pi

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Remember This!

Three cones fit exactly inside one cylinder of equal radius and height. So the volume of a cone is always exactly 1/3 the volume of the enclosing cylinder.

✏️ Try It!

An ice cream cone has radius 4 cm and height 9 cm. What is its volume in terms of π?

Practice with CalcVerse

📦Surface Area & Volume

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