What is the volume of the cone if S=5 and R=3?

1 Answer

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mlsiasebs | College Teacher | (Level 1) Associate Educator

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The formula to find the volume of a cone is

V = 1/3(pi)(r^2)(h)

where r is the radius and h is the height of the cone.  We are given the value of r but need to calculate the value of h from S.

Since h & r form the right angle in a triangle with S being the third side, we can use the Pythagorean theorem to solve for h.

r^2 + h^2 = S^2

3^2 + h^2 = 5^2

9 + h^2 = 25

h^2 = 16

h = 4

Now, that we know the value of r and h, we can calculate the volume

 V = 1/3(pi)(r^2)(h)

V = (1/3)(3.14)(3^2)(4)

V = (1/3)(3.14)(9)(4)

V = 37.7

You should have units on this answer but there were no units given in the problem.  If the original units were inches, then the answer will be in inches^3 (for example).