Big Ideas Math: Modeling Real Life, Grade 8
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Big Ideas Math: Modeling Real Life, Grade 8 View details
2. Volumes of Cones
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Exercise 14 Page 437

Use the formula for the volume of a cone.

≈ 115.5 yd^3

Practice makes perfect

We want to find the volume of a cone.

We can use the formula for the volume of a cone. V=1/3 B h Here, B is the area of the base and h is the height of the cone. Since the base is a circle, the area of the base will be equal to π r^2, where r is the radius. V= 1/3 π r^2 h We are given that the height of the cone is 9 yards and the diameter of the base is 7 yards. Note that if we divide the diameter by 2, we get the radius of the base. r=7/2= 3.5yd Let's substitute r= 3.5 and h= 9 into the formula and calculate the volume.
V=1/3π r^2 h
V=1/3π ( 3.5)^2 ( 9)
Evaluate right-hand side
V=1/3π(12.25)(9)
V=1/3π(110.25)
V=1/3(110.25π)
V=110.25π/3
V=36.75π
V=115.45353
V≈ 115.5
The volume of the cone is about 115.5 cubic yards.