Find the volume of a right circular cone that has a height of 12.5 cm and a base with a circumference of 5.8 cm. Round your answer to the ne

Question

Find the volume of a right circular cone that has a height of 12.5 cm and a base with a circumference of 5.8 cm. Round your answer to the nearest tenth of a cubic centimeter.

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Hadley 3 weeks 2021-09-07T02:00:43+00:00 2 Answers 0

Answers ( )

    0
    2021-09-07T02:02:01+00:00

    Answer:

    11.2 is the answer.

    Step-by-step explanation:

    0
    2021-09-07T02:02:10+00:00

    Answer:

    V = 11.2 cm^3

    Step-by-step explanation:

    Given

    Shape: Right Circular cone

    Height, h = 12.5 cm

    Base circumference, C = 5.8cm

    Required:

    Calculate Volume

    The volume of a cone is calculated as thus;

    Volume, V = \frac{1}{3}\pi r^2h

    Where V, r and h represent the volume, the radius and the height of the cone respectively

    But first we need to calculate the radius of the cone.

    Using formula of circumference.

    C = 2\pi r

    We have C to be 5.8cm

    By substituting this value;

    5.8 = 2\pi r

    Divide through by 2\pi

    \frac{5.8}{2\pi} = \frac{2\pi r}{2\pi}

    r = \frac{5.8}{2\pi}

    r = \frac{2.9}{\pi}

    Now, we can calculate the volume of the cone

    By substituting r = \frac{2.9}{\pi} and h = 12.5 cm;

    V = \frac{1}{3}\pi r^2h becomes

    V = \frac{1}{3}\pi * (\frac{2.9}{\pi})^2 * 12.5

    V = \frac{1}{3}\pi * \frac{8.41}{\pi^2} * 12.5

    V = \frac{1}{3} * \frac{8.41}{\pi} * 12.5

    Take \pi as 3.14

    V = \frac{1}{3} * \frac{8.41}{3.14} * 12.5

    V = 11.15976

    V = 11.2 cm^3 —- Approximated

    Hence, the volume of the cone is; V = 11.2 cm^3

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