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15 April, 09:55

The base of a cone has a radius of 4 millimeters and the height of the cone is 24 millimeters. What is the volume of the cone?

Question 6 options:

A. 32π mm3

B. 96π mm3

C. 128π mm3

D. 384π mm3

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Answers (1)
  1. 15 April, 13:54
    0
    The volume of the cone is 128π mm³ ⇒ answer (C)

    Step-by-step explanation:

    * Lets study the cone

    - Its base is a circle

    - Its height the perpendicular distance from its vertex to

    the center of the base

    - The length of its slant height = √ (h² + r²)

    - The volume of the con is 1/3 the volume of the cylinder

    ∵ The volume of the cylinder = πr²h

    ∴ The volume of the cone = (1/3) πr²h

    * In our problem:

    - r = 4 mm

    - h = 24 mm

    ∴ Its volume = (1/3) * π * (4) ² * 24 = 128π mm³

    * The volume of the cone is 128π mm³
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