Question

Some racquet balls are sold in cylindrical cans of three balls. Each ball has a diameter of 2.25 inches. The can has a diameter of 2.25 inches and is 6.75 inches tall. Find the volume of the empty space in the can. Use 3.14 for p. Round to the nearest hundredth.

Answer 1

1) Volume of each ball: [4/3]π(r^3) = [4/3]π(2.25/2)^3 = 5.96 in^3

2) Volume of 3 balss: 3*5.96 in^3 = 17.88 in^3

3) Volumen of the cylindrical can: [πr^2]h = π(2.25/2)^2 * 6.75 = 26.82 in^3

4) Empty space: 26.82 in^3 - 17.88 in^3 = 8.94 in^3

Answer 2

Answer:

Volume of the empty space =   6.95 $inches^{3}$

                                                 =   7 $inches^{3}$ (approx.)

Step-by-step explanation:

Volume of three spherical balls,

V = $V=3\times \frac{4}{3}\times \pi \times r^{3}$

$V=4\times 3.14\times \frac{2.25}{2}\times \frac{2.25}{2}\times \frac{2.25}{2}$

$V=17.88$ $inches^{3}$

Volume of the can, V = $\pi \times r^{2}\times h$

                                V =$3.14 \times \frac{2.25}{2}\times \frac{2.25}{2}\times6.25$

                                V = 24.83$inches^{3}$

Therefore, volume of the empty space = Volume of the can - volume of the three balls

                                                               = 24.83 - 17.88

                                                               = 6.95 $inches^{3}$

                                                               = 7 $inches^{3}$ (approx.)