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Shot put is a track-and-field event where athletes throw a heavy spherical ball. Shot put balls come in various sizes and materials. The diameter of a brass shot put ball is 4.2 inches
Part A
What is the volume of the brass shot put ball? Round your answer to the nearest cubic inch
Part B
The volume of a stainless steel shot put ball is 45 cubic inches. What is the approximate diameter of the stainless steel shot put ball? Round you answer to the nearest hundredth of an inch

Respuesta :

A) the volume would be 39 in³.
B) the diameter would be 4.42 in.

The formula for the volume of a sphere is V=4/3πr³:

V=4/3(3.14)(4.2/2)³
 = 4/3(3.14)(2.1)³ = 38.77 ≈ 39.

For part B, we use the given volume and work backward:
45 = 4/3(3.14)r³

Multiply both sides by 3:
45*3 = 4/3(3.14)r³*3
135 = 4(3.14)r³

Divide both sides by 4:
135/4 = 4(3.14)r³/4
33.75 = 3.14r³

Divide both sides by 3.14:
33.75/3.14 = 3.14r³/3.14
10.748 = r³

Take the cubed root of both sides:
∛10.748 = ∛r³
2.21 = r

Multiply this by 2, since d = 2r:
2.21*2 = 4.42

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