Question

5. A softball has a diameter of 8.3 in. How many softballs will fit inside of a storage unit 4 that is 15 feet wide, 10 feet long, and 5 feet high?

Answer 1

Answer:

4329 softballs

Step-by-step explanation:

To find the number of softballs that will fit into the container, we first find the volume of the softball. Since it is a sphere, its volume V = 4πr³/3 where r = radius = d/2 where d = diameter of softball.

So, V = 4π(d/2)³/3 = πd³/6

Since d = 8.3 in,

V =  πd³/6 =  π(8.3 in)³/6 = π × 571.787 in³/6 = 299.39 in³

The volume of the box, V' = 15 × 10 × 5 ft³ = 750 ft³ = 750 × (12 in)³ = 750 × 1,728 in³ = 1,296,000

So, for n softball to fit, its volume must equal the volume of the storage unit.

The volume of n softballs is nV.

For the softballs to fit, V' = nV

n = V'/V

= 1,296,000 in³/299.39 in³

= 4328.8 softballs

≅ 4329 softballs since we cannot have a decimal number of softballs.