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"A cylindrical canister contains 3 tennis balls. Its height is 8.75inches, and its radius is 1.5. The diameter of one tennis ball is 2.5. How much of the canister’s volume is unoccupied by tennis balls? Use 3.14 for π, and round your answer to the nearest hundredths place."

24.54in^3
37.28in^3
61.85in^3
7.56in^3

Respuesta :

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Find Volume of 1 tennis ball:
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Volume of 1 tennis ball = 4/3 x 3.14 x (2.5 ÷ 2)³

Volume of 1 tennis ball = 8.18 in³

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Find Volume of 3 tennis balls:
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Volume of 3 tennis balls = 8.18 x 3 = 24.54 in³

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Find Volume of teh cylindrical canister:
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Volume of the cylindrical canister = 3.14 x 1.5² x (2.5 x 3)

Volume of the cylindrical canister = 52.99 in³

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Find unoccupied space:
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Unoccupied space = 52.99 - 24.54

Unoccupied space = 28.45 in³

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Answer: 28.45 in³
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volume of 1 ball
= 4/3 x pi x radius^3
= 4/3 x 3.14 x 1.5^3
= 14.13 inches cubed

volume of all 3 balls
= 14.13 x 3
= 42.39 inches cubed

volume of cylinder
= pi x radius^2 x height
= 3.14 x 1.5^2 x 8.75
= 61.81875 inches cubed

volume of unoccupied space
= volume of cylinder - volume of all 3 balls
= 61.81875 - 42.39
= 19.42875 inches cubed

volume of unoccupied space/volume of cylinder (as a percentage)
= 19.42875/61.81875 x 100
= 31.42857143...
= 31.43% (to nearest hundredths place)

so 31.43% of the canister's volume is unoccupied by tennis balls

hope this helps! :)

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