The height $h$ and the base area $B$ of a cone are given. Find the volume of the cone. Write your answer in terms of $\pi$ .

Question

The height $h$ and the base area $B$ of a cone are given. Find the volume of the cone. Write your answer in terms of $\pi$ .

$h=6$ units

$B=4\pi$ square units

The volume is__ cubic units.

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Kim Chi 1 week 2023-01-23T20:29:21+00:00 2 Answers 0 views 0

Answers ( 2 )

  1. ngocdiep
    0
    2023-01-23T20:30:39+00:00
    Reply
    The height and the base area of the cone are 6 units and 4π square units. Then the volume of the cone is 24π.

    What is Geometry?

    It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
    The height (h = 6) and the base area (b = 4π) of a cone is given.
    Then the volume of the cone will be
    Volume = b × h
    Volume = 4π × 6
    Volume = 24π
    More about the geometry link is given below.

  2. ngocdiep
    0
    2023-01-23T20:31:04+00:00
    Reply
    Answer:
    (i) 84 cm.
    (ii) 5635π cm^2
    Step-by-step explanation:
    (i)
    The volume of the cone = 1/3 π r^2 h
    = 1/3 π 35^2 h.
    The volume of the hemisphere = 2/3 π 35^3.
    As the volume of the cone is 1 1/5 ( = 6/5) times the volume of the hemisphere:
    1/3 π 35^2 h = 2/3 π 35^3 * 6/5
    h = 2/3 π 35^3 * 6/5 / 1/3 π 35^2
    h = 84 cm (answer).
    (ii) Surface area of the hemisphere = 2 π * 35^2 = 2450π cm^2.
    Surface area of the cone = π r l where l = slant height.
    l = √(35^2 + 84^2) = 91 cm.
    So the surface area of the cone = 35*91 π = 3185π.
    So the total surface area of the solid is 3185π + 2450π
    = 5635π cm^2.
    i hope this work for you

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