how to find the surface area of a cone with a diameter of 8 and a slant height of 7? with steps? please
don't know what steps you want. The area of a cone is
a = 2πr(r+s)
just plug in the values for r and s
To find the surface area of a cone, you need to know the diameter and the slant height. The formula for the surface area of a cone is:
Surface Area = πr² + πrℓ
Where r represents the radius of the base of the cone, and ℓ represents the slant height.
Let's calculate the surface area of the cone with a diameter of 8 and a slant height of 7 using the steps below:
Step 1: Find the radius (r) of the cone:
The diameter of the cone is 8, and the formula for finding the radius from the diameter is:
radius = diameter / 2
So, r = 8 / 2 = 4.
Step 2: Find the base area of the cone:
The formula for the area of a circle is:
Area = πr²
So, the area of the base of the cone is:
Base Area = π(4)² = 16π.
Step 3: Find the lateral surface area of the cone:
The formula for the lateral surface area of a cone is:
Lateral Surface Area = πrℓ.
So, the lateral surface area of the cone is:
Lateral Surface Area = π(4)(7) = 28π.
Step 4: Calculate the total surface area:
To find the total surface area of the cone, add the base area and the lateral surface area:
Total Surface Area = Base Area + Lateral Surface Area
= 16π + 28π
= 44π.
Therefore, the surface area of the cone with a diameter of 8 and a slant height of 7 is 44π, which is the final answer.