Find in terms of π the curved surface area of a cone diameter 10cm and height 12cm?

The formula for the curved surface area of a cone is πrl, where r is the radius of the base and l is the slant height of the cone.

Given that the diameter of the cone is 10cm, the radius (r) is half of the diameter, so r = 5cm.

To find the slant height (l), we can use the Pythagorean theorem. The slant height, the height, and the radius form a right triangle. So, l^2 = r^2 + h^2, where h is the height of the cone.

Substitute the values we have:
l^2 = 5^2 + 12^2
l^2 = 25 + 144
l^2 = 169
l = √169
l = 13cm

Now, we can calculate the curved surface area:
Curved surface area = πrl
Curved surface area = π * 5 * 13
Curved surface area = 65π cm^2

Therefore, the curved surface area of the cone is 65π cm^2.

The curved surface area of a cone is given by the formula:

$$A = \pi r l$$

where:

- A is the curved surface area
- r is the radius of the base
- l is the slant height

In this case, the diameter of the base is 10cm, so the radius is 5cm. The slant height can be found using the Pythagorean theorem:

$$l = \sqrt{h^2 + r^2}$$

where h is the height of the cone. Substituting the given values, we get:

$$l = \sqrt{12^2 + 5^2} = 13cm$$

Now we can calculate the curved surface area:

$$A = \pi r l = \pi (5cm)(13cm) = 65\pi cm^2$$

Therefore, the curved surface area of the cone is 65π cm^2.