For a cone with radius 3 cm and slant 5 cm, what is the volume and total surface area?

Given the radius of a cone is r= 3
cm

The slant s = 5 cm

We need to find
the volume and the surface area.

First we will calculate the surface
area.

The surface area of the cone = surface area of the base +
surface area of the slant.

==> Surface area of the base = r^2
* pi = 3^2 pi = 9pi

==> surface area of the slant = r*s*pi
3*5*pi = 15pi.

==> Then the total surface area = 15pi + 9pi =
24pi

Now we will determine the
volume.

We know that :

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

==> We will calculate the height
h.

==> h= sqrt( s^2 -r^2) = sqrt(25-9) = sqrt16 =
4

==> h= 4

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

= (1/3)* 9 * 4 * pi =
12pi.

Then the volume of the cone is 12pi cm^3 and the
surface area is 24pi cm^3.