Question

Plss help its due in 2 days :(

A toy shop is manufacturing hollow plastic spheres. The outside diameter of the sphere is 6 inches and the thickness of material is 1 inch. The spheres are packaged in boxes of 8, and the density of the material is 3.25 g/in3. What is the weight of the box to the nearest gram?

Answer 1

2069 grams

Explanation:

Assume that the box itself is massless so the weight is only due to the spheres only. Calculate the volume of a solid sphere of radius 3 in:

Vout = (4/3)pi(3^3) = 36pi in^3

Now calculate the volume of a solid sphere of radius 2 in:

Vin = (4/3)pi(2^3) = (32/3)pi in^3

To calculate the volume of the hollow sphere, subtract Vin from Vout:

Vnet = Vout - Vin = (76/3)pi

Since the density of the plastic is 3.25 g/in^3, the mass of each hollow sphere is

m = (density) × Vnet = (3.25 g/in^3)×(76/3)pi

= 258.7 g

Since there are 8 spheres in a box, the total weight of the box is

M = 8m = 2069 grams