Find Volume of Spheres

Students apply V = (4/3)πr³ to compute volumes of spheres and solve for the radius when given the volume. They compare sphere volumes to cylinders with the same radius and height equal to the diameter, discovering the 2:3 volume ratio.

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Grade 8 · Geometry: Volume · question 1 of 3

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V = (4/3) × 3.14 × 1.5^3 =

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A sphere is a round solid with every surface point equally far from the center.

Volume uses the radius cubed, times 4/3 pi.

Read it: Volume of a sphere

A sphere's volume is 4 × π × r^3 ÷ 3. For radius 6: 6 × 6 × 6 = 216, times 4 is 864, divided by 3 is 288, and 288 × 3.14 = 904.32 cubic units.

Multiply the radius by itself 3 times: that is r^3.
Multiply by 4, then divide by 3.
Multiply by 3.14, or keep π beside the number.

r^3 means r × r × r: 6 × 6 × 6 = 216.

4 × 216 = 864 and 864 ÷ 3 = 288, so the volume is 288π.

With π as 3.14, 288 × 3.14 = 904.32 cubic units.

Sphere volume: V = 4 × π × r^3 ÷ 3.

Reading r^3 as r × 3: 6 × 3 = 18.

r^3 is the radius used 3 times: 6 × 6 × 6 = 216.

A sphere has radius 3. With π as 3.14, its volume is ___ cubic units. — 113.04. 3 × 3 × 3 = 27, × 4 ÷ 3 = 36, and 36 × 3.14 = 113.04.

V = (4/3)π(3)³

Look at this ball with radius three centimeters. How much space does it take up inside?

Grade 8 · Sphere with radius 3 cm

The volume of any sphere is four-thirds times pi times r cubed.

Our radius is three, so we substitute three in for r.

Three cubed means three times three times three, which is twenty-seven.

Four-thirds of twenty-seven is thirty-six. So the volume equals thirty-six pi.

Using pi about three point one four, thirty-six pi is about one hundred thirteen.

The sphere holds about one hundred thirteen cubic centimeters. Nice work!

What you see

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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.

An example week.

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