what's the surface area of a cone with a diameter of 25 and a slant height of 22 use 3.14 for pi
The surface area of a cone consists of two parts: the lateral or side area and the base area.
The formula for the lateral surface area of a cone is given by:
A_lateral = π * r * l
where r is the radius of the base of the cone and l is the slant height.
The formula for the base area of a cone (which is a circle) is:
A_base = π * r^2
Since we are given the diameter, we can find the radius by dividing the diameter by 2. So if the diameter is 25, the radius is:
r = diameter / 2
r = 25 / 2
r = 12.5
Now, using the provided slant height (l) of 22 and the value of π as 3.14, we can plug the values into the formulas:
A_lateral = π * r * l = 3.14 * 12.5 * 22
A_lateral = 3.14 * 275
A_lateral ≈ 862.5
A_base = π * r^2 = 3.14 * (12.5)^2
A_base = 3.14 * 156.25
A_base ≈ 490.625
Finally, to find the total surface area of the cone, we add the lateral surface area and the base area together:
A_total = A_lateral + A_base
A_total ≈ 862.5 + 490.625
A_total ≈ 1353.125
So the total surface area of the cone is approximately 1353.125 square units.