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Math Asked by a SnapAndSolve user · 15 minutes ago

For the three-part question that follows, provide your answer to each part in the given workspace. Identify...

For the three-part question that follows, provide your answer to each part in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
The volume of a cone is calculated using the formula \( V = \frac{1}{3} \pi r^2 h \), where \( r \) is the radius of the cone and \( h \) is the height of the cone.
Part A: The Creamery sells an ice cream cone that is 25 cm tall with a radius of 9 cm. What is the volume of ice cream that fits inside the cone? Use 3.14 for \( \pi \). Show your work.
Part B: Suppose The Creamery would like to create a smaller cone for kids that has a volume of 1272 cm³. If the radius of the cone remains at 9 cm, calculate the new height of the cone. Use 3.14 for \( \pi \). Round to the nearest hundredth.
Part C: Show your work to support your answer to Part B.

Answer

  1. Part A:

    To find the volume of the cone, use the formula \( V = \frac{1}{3} \pi r^2 h \).
    \( r = 9 \) cm, \( h = 25 \) cm, and \( \pi = 3.14 \).
    \( V = \frac{1}{3} \times 3.14 \times 9^2 \times 25 \)
    \( V = \frac{1}{3} \times 3.14 \times 81 \times 25 \)
    \( V = \frac{1}{3} \times 3.14 \times 2025 \)
    \( V = \frac{1}{3} \times 6358.5 \)
    \( V = 2119.5 \) cm³

  2. Part B:

    Given the volume \( V = 1272 \) cm³ and \( r = 9 \) cm, find the height \( h \).
    Use the formula \( V = \frac{1}{3} \pi r^2 h \).
    \( 1272 = \frac{1}{3} \times 3.14 \times 9^2 \times h \)
    \( 1272 = \frac{1}{3} \times 3.14 \times 81 \times h \)
    \( 1272 = \frac{1}{3} \times 254.34 \times h \)
    \( 1272 = 84.78 \times h \)
    \( h = \frac{1272}{84.78} \)
    \( h \approx 15.00 \) cm

  3. Part C:

    Show the calculation steps:
    \( 1272 = \frac{1}{3} \times 3.14 \times 81 \times h \)
    \( 1272 = 84.78 \times h \)
    \( h = \frac{1272}{84.78} \)
    \( h \approx 15.00 \) cm

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