Question

The radius of the cone is 5 in and y = 13 in. What is the volume of the cone in terms of π?

Answer 1

Answer:

The volume of the cone is;

100 π inches^3

Step-by-step explanation:

To calculate the volume, we need the height

We can get the height from the slant height and the radius

Mathematically, we use Pythagoras’ theorem for this as the slant height, the radius and the height forms a right-angled triangle

The right-angled triangle has the slant height as its hypotenuse

By the theorem, the square of the hypotenuse equals the sum of the squares of the two other sides

Let the height be h

Thus;

12^2 = 5^2 + h^2

169= 25 + h^2

h^2 = 169-25

h^2 = 144

h = √1144 inches = 12 inches

The volume of the cone is;

1/3 * π * r^2 * h

= 1/3 * π * 5^2 * 12

= 100 π inches^3