Question

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Calculator
Cone X has a diameter of 20 ft and a height of 16 ft. Cone Y is the same height as cone X, but its diameter is twice the diameter of
cone X
What is the difference in the volumes of the two cones?
Use 3.14
05.024 ft
15.072 ft
O 20.096 ft
3.01 Readiness Checkpoint: Volumes of Cylinders and Cones Di
I don't know
2 3
4 Finish

Answer 1

(a) 5024 ft³

Explanation:

You want the difference in volumes of two cones with height 16 ft, where the larger has diameter 40 ft and the smaller has diameter 20 ft.

Volume

The volume of a cone is given in terms of its radius as ...

V = π/3(r²h) . . . . . . r=radius; h=height

The radius is half the diameter, so the formula with diameter is ...

V = π/3(d/2)²h = π/12d²h

Difference

The two given cones have the same height, but different diameters. The difference in volumes will be ...

V2 -V1 = (π/12)((d2)²h) -(π/12)((d1)²h) = (πh/12)((d2)² -(d1)²)

V2 -V1 = 3.14(16 ft)/12 × ((40 ft)² -(20 ft)²) = 3.14·16/12·1200 ft³

= 3.14·1600 ft³ = 5024 ft³

The difference in volumes of the two cones is 5025 cubic feet.