Volume of cylinders, cones, and spheres (Geometry) · lesson

Cylinders: base times height

💡 A cylinder's volume is the circle area times the height: V = πr²h.

A cylinder is a stack of equal circles. The area of one circle is πr². Multiply by the height to stack them up.

If you know the volume and want the height, put the numbers into V = πr²h and divide.

Some questions want the answer as a number times π. Then type only the number in front of π.

🧠 Let's work it out

A cylinder has radius 2 and height 7. Find its volume.

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💡 A cone holds one third of the cylinder with the same base and height: V = (1/3)πr²h.

Fill a cone with water and pour it into a cylinder of the same size. It takes three cones to fill the cylinder.

To find a missing height, set (1/3)πr²h equal to the volume. If the volume is given as a number times π, the π cancels on both sides.

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A cone has radius 3 and height 8. Find its volume.

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💡 A sphere's volume is (4/3)πr³, and a half sphere holds half of that.

A sphere is a ball. Its volume uses the radius cubed, r × r × r.

A hemisphere is half a sphere, like a bowl or a dome. Find the full sphere's volume and divide by 2.

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A sphere has radius 2. Find its volume.

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💡 Add the volumes of the parts, and when material is reshaped the volume stays the same.

A silo might be a cylinder with a half sphere on top. Find each part's volume and add them.

When metal is melted and poured into a new shape, none is lost. Set the old volume equal to the new volume and solve for the missing length.

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A ball of radius 9 is melted into a cylinder of radius 6. How tall is the cylinder?

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