Surface Area and Volume • Topic 3 of 7

Cylinders

A cylinder has two circular bases joined by a curved surface. Its volume is the base area times the height: πr²h, where r is the base radius and h the height. The SAT usually wants the answer in terms of π. For radius 3 and height 5, the volume is π(3²)(5) = 45π. Square the radius first, then multiply by the height and attach π. If a diameter is given, halve it to get r before squaring. Cylinder volume appears in tank, can and pipe problems. Keep πr²h (volume) distinct from the curved surface area 2πrh, which the SAT asks for less often.

A cylinder with radius and heightCylinderrhVolume = πr²h

✅ Solved examples

1. A cylinder has radius 3 and height 5. Find its volume in terms of π.
π(3²)(5) = 45π.
2. A cylinder has radius 2 and height 10. Find its volume.
π(4)(10) = 40π.
3. A cylinder has radius 5 and height 4. Find its volume.
π(25)(4) = 100π.
4. A cylinder has radius 1 and height 9. Find its volume.
π(1)(9) = 9π.

✏️ Practice — try these, take hints as needed

1. A cylinder has radius 4 and height 3. Find its volume in terms of π.
πr²h.
π(16)(3).
—
48π.
2. A cylinder has radius 2 and height 6. Find its volume.
π(4)(6).
—
—
24π.
3. A cylinder has radius 3 and height 10. Find its volume.
π(9)(10).
—
—
90π.
4. A cylinder has radius 6 and height 2. Find its volume.
π(36)(2).
—
—
72π.
5. A cylinder has radius 5 and height 8. Find its volume.
π(25)(8).
—
—
200π.

📝 Topic test — 8 questions

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