Question

An art student wishes to create a clay sphere as part of a sculpture. If the clay’s density is approximately 88 pounds per cubic foot and the sphere’s radius is 2 feet, what is the weight of the sphere to the nearest pound? Use 3.14 for pi, and enter the number only.

Answer 1

The weight of the sphere = 2947 pounds

Explanation:

* Lets revise the volume of the sphere

- The volume of the sphere is 4/3 π r³, where r is the radius of

the sphere

- Density = mass ÷ volume

- Mass is the weight and volume is the size, so density is weight

divided through size

- Density = weight ÷ volume

* Now lets solve the problem

∵ The clay's density ≅ 88 pounds/cubic foot

∵ The radius of the sphere is 2 feet

∵ The volume of the sphere = 4/3 π r³

∴ The volume of the sphere = 4/3 π (2)³ = 32/3 π feet³

∵ Density = weight/volume ⇒ by using cross multiply

∴ Weight = density × volume

∵ Density = 88 pounds/foot³

∵ Volume = 32/3 π feet³

∵ π = 3.14

∴ The weight of the sphere = 88 × 32/3 × 3.14 = 2947 pounds