Find Volume of Cylinders

Students derive and apply V = πr²h to compute the volume of cylinders, interpreting the formula as the area of the circular base times the height. They solve for volume given radius and height, or solve for a missing dimension given the volume.

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Grade 8 · Geometry: Volume · question 1 of 3

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V = 3.14 × 1^2 × 11 =

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Cylinder volume is the circle's area times the height.

The circle's area is pi times radius times radius.

Read it: Volume of a cylinder

A cylinder with radius 3 and height 5 is layers of its base circle. The base is π × 3 × 3; with π as 3.14, that is 28.26. There are 5 layers: 28.26 × 5 = 141.3 cubic units.

Find the base circle's area: π × r × r.
Multiply the base by the height.
Use 3.14 for π, or keep π beside the number, as the problem asks.

Each slice 1 unit thick holds the base circle's area in cubic units, and the height counts the slices.

r × r is the radius times itself: 3 × 3 = 9, so the base is 3.14 × 9 = 28.26.

So V = π × r × r × h, and for this cylinder that is 28.26 × 5 = 141.3.

Cylinder volume: V = π × r × r × h, the base circle times the height.

Doubling the radius instead of multiplying it by itself: 3.14 × 3 × 2 = 18.84, and 18.84 × 5 = 94.2.

r × r is the radius times itself: 3 × 3 = 9, so the base is 3.14 × 9 = 28.26, and 28.26 × 5 = 141.3.

A cylinder has radius 6 and height 12. With π as 3.14, its volume is ___ cubic units. — 1356.48. The base circle: 3.14 × 6 × 6 = 113.04. Times the height: 113.04 × 12 = 1356.48.

r = 3 cm, h = 10 cm

Look at this soup can with a radius of three centimeters and a height of ten centimeters. How much soup fits inside?

Grade 8 · How much soup fits in a can?

Here's our cylinder — a round base on the bottom, the same circle on top, and straight sides connecting them.

The volume of any cylinder equals pi times the radius squared times the height.

The first part — pi r squared — is the area of the round base, the circle on the bottom.

Our radius is three, so r squared is nine. The base area is nine pi square centimeters.

Now we stack that base up the full height of the can — ten centimeters tall.

Multiply nine pi by ten. Nine pi times ten equals ninety pi.

Using pi about three point one four, ninety pi is about two hundred eighty-three.

The volume is ninety pi — about two hundred eighty-three cubic centimeters of soup. Nice work!

Now you try. Count this cylinder's flat faces. How many faces are flat?

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MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

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MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

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