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ella [17]
3 years ago
15

"A cylindrical canister contains 3 tennis balls. Its height is 8.75inches, and its radius is 1.5. The diameter of one tennis bal

l 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
Mathematics
2 answers:
puteri [66]3 years ago
8 0
----------------------------------------------
Find Volume of 1 tennis ball:
----------------------------------------------
Volume of 1 tennis ball = 4/3 x 3.14 x (2.5 ÷ 2)³

Volume of 1 tennis ball = 8.18 in³

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

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

Volume of the cylindrical canister = 52.99 in³

----------------------------------------------
Find unoccupied space:
----------------------------------------------
Unoccupied space = 52.99 - 24.54

Unoccupied space = 28.45 in³

----------------------------------------------
Answer: 28.45 in³
----------------------------------------------


Aloiza [94]3 years ago
5 0
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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