# 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

Relevance

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

• 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

• slant length ℓ = 5 cm

height h = √(ℓ²-r²) = √(5²-3²) = 4 cm

volume V = ⅓πr²h = ⅓π3²·4 = 12π cm³

• 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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