Artist makes sculpture

Question

An artist wants to make a plastic sphere for a sculpture. The plastic weighs 0.8 ounces per cubic inch. The maximum weight of the sphere is to be 80 pounds. The formula for the volume V of a sphere is V=4/3 pi r cubed, where r is the radius of the sphere. What is the maximum radius the sphere can have?

Answer 1

Wp=.8oz/in³ 

Vs=4/3•πr ³ 

Ws=V•(8oz/in³)

Ws=(4/3•πr³)•(8oz/in³)=80lbs

 

remember the unit conversion 

16oz=1lbs

 

Ws=80lbs•(16oz/1lbs)

=(4/3•πr³)•(8oz/in³)

 

Solve for r

 

80•16oz=(4/3•πr³)•(8oz/in³)

120in ³ =πr ³ 

3.37in=r

 

That makes the volume 

V=160in³