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mamaluj [8]
3 years ago
8

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.
Mathematics
2 answers:
kicyunya [14]3 years ago
8 0

Volume of 1 ball = 4/3 π r³ = 4/3 (3.14) (2.25 ÷ 2)³ = 5.961 in³


Volume of 3 balls = 5.961 x 3 = 17.883 in³


Volume of cylinder = πr²h = (3.14) (2.25 ÷ 2)² (6.75) = 26.825 in³


Empty Space = 26.825 - 17.883 = 8.94 in³ (nearest hundredth)


Answer: 8.94 in³

Romashka [77]3 years ago
6 0
In order to find the empty space we need to find the total space and the filled space.

The formula we use to find the volume of the cans or any cylinder is:
\pi {r}^{2} h
Plug in the givens:
3.14 \times  {1.125}^{2}  \times 6.75
Simplify:

3.14 \times 1.265625 \times 6.75 = 26.824921875

Now let's find the balls' volume. These cans can hold 3 balls:

n \times  \frac{4}{3} \pi {r}^{3}  \\  \\ 3 \times  \frac{4}{3}  \times 3.14 \times  {1.125}^{3}
Take the cube:
3 \times  \frac{4}{3}  \times 3.14 \times  1.423828125
Solve:
3 \times  \frac{4}{3}  \times 3.14 \times  1.423828125 = 17.88328125
To find the empty space:
26.824921875 - 17.88328125 = 8.941640625
The empty space is 8.94 in3.
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