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16 July, 02:18

A cone has a volume of 50π in3 and a diameter of 10 in. Wilson states that a cylinder with the same height and diameter has the same volume. Which statement explains whether or not Wilson is correct? A cylinder in which h = 2 and d = 10 has a volume of 50π in3; therefore, Wilson is incorrect. A cylinder in which h = 6 and d = 10 has a volume of 50π in3; therefore, Wilson is incorrect. A cylinder in which h = 2 and d = 10 has a volume of 150π in3; therefore, Wilson is incorrect. A cylinder in which h = 6 and d = 10 has a volume of 150π in3; therefore, Wilson is incorrect.

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  1. 16 July, 05:46
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    A cylinder in which h = 6 and d = 10 has a volume of 150π in³; therefore, Wilson is incorrect ⇒ last answer

    Step-by-step explanation:

    * Lets revise the volume of the cone and the cylinder

    - The volume of cone is 1/3 πr²h, where r is its radius and h is its height

    - The volume of the cylinder is πr²h

    * Lets solve the problem

    ∵ The cone has a volume 50π inches³

    ∵ The diameter of the cone is 10 inches

    ∵ The diameter is twice the radius

    ∴ 2r = 10 ⇒ divide both sides by 2

    ∴ r = 5

    ∵ The rule of the volume of the cone = 1/3 πr²h

    ∴ 50π = 1/3 π (5²) h

    ∵ 50π = 1/3 (25π) h ⇒ divide both sides by 25π

    ∴ 2 = 1/3 h ⇒ multiply both sides by 3

    ∴ 6 = h

    ∴ The height of the cone is 6 inches

    - The cylinder has the same diameter and the same height of the cone

    ∵ The diameter of the cone = 10 inches

    ∵ The height of the cone = 6 inches

    ∴ The diameter of the cylinder is 10 inches

    ∴ The height of the cylinder is 6 inches

    ∵ The rule of the volume of the cylinder is πr²h

    ∵ The radius of the cylinder = 10/2 = 5 inches

    ∴ The volume of the cylinder = π (5²) (6) = 150π inches³

    * The volume of the cylinder not equal the volume of the cone

    ∴ A cylinder in which h = 6 and d = 10 has a volume of 150π in³;

    therefore, Wilson is incorrect.
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