Which of the following is the lateral surface area of the cone whose height is 12cm and slant height 12cm?

To find the lateral surface area of a cone, we use the formula:

Lateral Surface Area = πr * l

where r is the radius of the base of the cone and l is the slant height.

Given that the slant height is 12cm, we can use the Pythagorean theorem to find the radius:

r^2 + h^2 = l^2
r^2 + 12^2 = 12^2
r^2 + 144 = 144
r^2 = 0
r = 0

Since the radius is 0, the lateral surface area of the cone is also 0.

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

$$L = \pi r l$$

where:

- L is the lateral surface area
- r is the radius of the base
- l is the slant height

We are given that the height of the cone is 12 cm and the slant height is 12 cm. We can use the Pythagorean theorem to find the radius of the base:

$$r^2 + h^2 = l^2$$

$$r^2 + 12^2 = 15^2$$

$$r^2 = 25$$

$$r = 5$$

Now we can plug in the values for r and l into the formula for the lateral surface area:

$$L = \pi (5)(12)$$

$$L = 60\pi$$

Therefore, the lateral surface area of the cone is 60π cm^2.