A cone has a diameter of 6 cm and a slant height of 5 cm. What is the exact volume (in cubic centimeters) of the cone?....?

A cone has a diameter of 6 cm and a slant height of 5 cm. What is the exact volume (in cubic

centimeters) of the cone?

a. 80/3 pi

b. 16 pi 

c. 12 pi

d. 15 pi

4 Answers

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  • 6 months ago
    Favorite Answer

    V = 1/3 πr²h

    r = radius iof the base

    h = vertical height

    The slant height represents the hypotenuse of the right triangle with legs r and h

    r² + h² = s²

    3² + h² = 5²

    h = 4 cm

    V = 1/3 π(3)²(4)

    V = 12π

    Answer C

  • 6 months ago

    given r = 6/2 = 3 cm

    s = 5 cm

    solving the height of the cone by pythagorean theorem

    h = √(s^2 - r^2)

    h = √(5^2 - 3^2) =

    h = √(16)

    h = 4 cm

    solving the volume of the cone

    V = 1/3πr^2h

    V = 1/3π(3)^2(4)

    V = 12π cm^3

    Answer is c. 12 pi

  • DWRead
    Lv 7
    6 months ago

    slant length ℓ = 5 cm

    height h = √(ℓ²-r²) = √(5²-3²) = 4 cm

    volume V = ⅓πr²h = ⅓π3²·4 = 12π cm³

  • 6 months ago

    If the slant height is 5 and the radius is 3, then the height is 4

    This is because we have a 3, 4, 5 pythagorean triple

    Now, Volume is (1/3)πr²h

    so, (1/3)π(3)²(4)

    or, (1/3)(36)π

    i.e. 12π cm³

    :)> 

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