Question

Craig is constructing weights of different sizes to use in his home gym. One such weight is a solid steel sphere with a radius of 3.5 inches. The density of steel is 0.284 pounds per cubic inch. What is the approximate
mass of the spherical weight?
A. 51 pounds
B. 77 pounds
C. 15 pounds
D. 44 pounds

Answer 1

The approximate mass of the spherical weight is 51 pounds

To answer the question, we need to know what the mass of the sphere is

Mass of the sphere

The mass of the sphere m = ρV where

• ρ = density of steel = 0.284 lb/in³ and
• V = volume of sphere = 4πr³/3 where
• r = radius of sphere = 3.5 in

So, m = ρV

= ρ4πr³/3

Substituting the values of the variables into the equation, we have

m = ρ4πr³/3

= 0.284 lb/in³ × 4π(3.5 in)³/3

= 0.284 lb/in³ × 4π × 42.875 in³/3

= 48.706π lb/3

= 153.014 lb/3

= 51 lb

The approximate mass of the spherical weight is 51 pounds

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