I need to know the steps on how to solve the surface area of a cone. That has a radius of 4 and a height of 7.
http://www.ducksters.com/kidsmath/finding_the_volume_surface_area_of_a_cone.php
Thank you your a lifesaver
You're welcome.
To find the surface area of a cone, follow these steps:
Step 1: Find the slant height of the cone using the Pythagorean theorem.
The slant height (l) is the distance from the tip of the cone to any point on the base edge. To find it, use the Pythagorean theorem:
l² = r² + h²
Where:
- l is the slant height,
- r is the radius of the base of the cone, and
- h is the height of the cone.
In your case, the radius (r) is 4 and the height (h) is 7, so substitute these values into the equation:
l² = 4² + 7²
l² = 16 + 49
l² = 65
Taking the square root of both sides gives us:
l ≈ √65
Step 2: Calculate the base area of the cone.
The base area (A) of a cone is given by the formula:
A = πr²
Substitute the radius (r) into the equation:
A = π(4)²
A = π(16)
A = 16π
Step 3: Calculate the lateral surface area of the cone.
The lateral surface area (B) of a cone is half the product of the slant height (l) and the circumference (C) of the base of the cone:
B = 1/2 × l × C
To find C, we use the formula for the circumference of a circle:
C = 2πr
In your case, the radius (r) is 4, so substitute it into the equation:
C = 2π(4)
C = 8π
Now substitute the values of l and C into the equation to find the lateral surface area (B):
B = 1/2 × √65 × 8π
B ≈ 4√65π
Step 4: Calculate the surface area of the cone.
Finally, to get the overall surface area of the cone (S), add the base area (A) and the lateral surface area (B):
S = A + B
S = 16π + 4√65π
This is your solution. Simplify further if required.