Question

What is the volume of a cone with a radius of 3 feet and a slant height of 6 feet? Use full value for pi. Round your answer to the nearest hundredth. (4 points)

Answer 1

The volume of this cone is 48.91 cubic feet.

Explanation:

In order to calculate the volume of this cone we need to use the appropriate formula as shown bellow:

Volume = (1/3)*pi*r²*h

But we have the slant height of the cone and not the height needed, in order to calculate that that we must use Pytagora's theorem, where the slant height is the hypothenuse, the radius of the base is one of the cathetus and the height of the cone is the other so we have:

6² = 3² + h²

h² = 36 -9 = 27

h = sqrt(27) = 3*sqrt(3)

So the volume is:

Volume = (1/3)*pi*(3)²*3*sqrt(3) = pi*9*sqrt(3) = 9*1.73*pi

Volume = 15.57*3.14159 = 48.91 cubic feet.

The volume of this cone is 48.91 cubic feet.

Answer 2

48.9 ft³

Explanation:

Volume of a cone can be determined by

V= πr² h/3

where

radius 'r' = 3feet

But we need to find height 'h'

If you see the figure in the attachment, the triangle is right angle.

Where,

slant height is hypotenuse

radius is base

height is perpendicular

Therefore, by using Pythagoras theorem

6² = 3² + h²

h² = 36 -9 = 27

h = √(27) = 3√3

Put the value of h in Volume of cone equation.

V= π3² (3√3) / 3

V=48.9 ft³

Therefore, The volume of this cone is 48.91ft³