what is the surface area of a right cone with a diameter of 15 units and a slant height of 34 units.

To find the surface area of a right cone, you'll need to know its slant height and the radius of its base.

First, let's find the radius of the base. The diameter of the cone is given as 15 units, and we know that the radius is half the diameter.

Radius = Diameter/2 = 15/2 = 7.5 units

Next, we can use the slant height and radius to find the height of the cone using the Pythagorean theorem. The slant height is the hypotenuse of a right triangle, with the radius as one of the legs.

Using the Pythagorean theorem:
Height^2 + Radius^2 = Slant height^2

Height^2 + 7.5^2 = 34^2
Height^2 + 56.25 = 1156
Height^2 = 1156 - 56.25
Height^2 = 1099.75

Taking the square root of both sides:
Height ≈ √1099.75 ≈ 33.15

Now that we have the radius (7.5 units) and the height (33.15 units), we can calculate the surface area of the cone.

The surface area of a cone can be calculated using the formula:
Surface Area = π * r * (r + h)

Surface Area = π * 7.5 * (7.5 + 33.15)
Surface Area ≈ 3.14159 * 7.5 * 40.65
Surface Area ≈ 956.54 square units

Therefore, the surface area of the given cone is approximately 956.54 square units.

http://www.mathopenref.com/conearea.html

I'll be glad to check your answer.