This figure shows a can of three tennis balls. The can is just large enough so that the tennis balls will fit inside with the lid on. The diameter of each tennis ball is 2.5 in. Find the percent of the can occupied by the tennis balls.

The volume of the can and the volume of the tennis balls both need to be found.

  1. The formula for the volume of a cylinder is _____.
  2. The formula for the area of the base is _____.
  3. The area of the base in terms of π is _____.
  4. The height of the tennis ball container is _____.
  5. The volume of the cylinder is _____.
  6. To find the volume of the tennis ball, the formula for the volume of a sphere is used. The volume of one tennis ball is _____.
  7. The volume of three tennis balls is _____.
  8. To find the percent of the can occupied by the tennis balls, the volume of the _____ is divided by the volume of the _____.
  9. The percent of the can occupied by the tennis balls is _____.

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Check Your Answers

  1. The formula for the volume of a cylinder is

    V = Bh.

  2. The formula for the area of the base is

    A = πr2

  3. The area of the base in terms of π is

    A = πr2 = π(1.25)2 = 1.56π sq in

  4. The height of the tennis ball container is

    2.5 + 2.5 + 2.5 = 7.5 in

  5. The volume of the cylinder is

    V = Bh = 1.56 π (7.5) = 11.7 π cu in

  6. To find the volume of the tennis ball the formula for the volume of a sphere is used. The volume of one tennis ball is

    V = 4 3π r3 = 4 3π(1.25)3 = 4 3π 1.95 = 2.6π cu in
  7. The volume of three tennis balls is

    3V = 3(2.6π) = 7.8π cu in

  8. To find the percent of the can occupied by the tennis balls the volume of the tennis balls is divided by the volume of the can.

  9. The percent of the can occupied by the tennis balls is

    (7.8π cu in) ÷ (11.7π cu in) = .67 ⇒ 67%

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