Question

The senior class want to play a practical joke on the principal, who was a former college basketball star. They want to fill his office full of basketballs. The diameter of a basket ball is 9.5 inches. The dimensions for his office are 20 feet long, 18 feet wide and 12 feet tall. If you assume there is not furniture in the office, then approximately how many basketballs would it take to fill up his entire office to the ceiling? (Model the basketball as a sphere).

Answer 1

The number of basketball that will fill up the entire office is approximately 16,615.

Recall:

Volume of a spherical shape = $\frac{4}{3} \pi r^3$

Volume of a rectangular prism = $l \times w \times h$

Given:

Diameter of basketball = 9.5 in.

Radius of the ball = 1/2 of 9.5 = 4.75 in.

Radius of the ball in ft = 0.4 ft (12 inches = 1 ft)

Dimension of the office (rectangular prism) = 20 ft by 18 ft by 12 ft

• First, find the volume of the basketball:

Volume of ball = $\frac{4}{3} \pi r^3 = \frac{4}{3} \times \pi \times 4.75^3$

Volume of basketball = $448.92 in^3$

• Convert to $ft^3$

$1728 in.^3 = 1 ft^3$

Therefore,

• Volume of basketball = $\frac{448.92}{1728} = 0.26 ft^3$

• Find the volume of the office (rectangular prism):

Volume of the office = $20 \times 18 \times 12 = 4,320 ft^3$

• Number of basket ball that will fill the office = Volume of office / volume of basketball

• Thus:

Number of basket ball that will fill the office = $\frac{4,320}{0.26} = 16,615$

Therefore, it will take approximately 16,615 balls to fill up the entire office.

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