What the surface area of a cone with a diameter of 8 and height of 7

with base radius r, the total area is

πr^2 + πrs
where s^2 = r^2+h^2

Just plug in your numbers

I got 784 dudes

To find the surface area of a cone, we need to calculate the lateral surface area and add it to the base area. The formula for the lateral surface area of a cone is given by A = πrℓ, where r is the radius of the base and ℓ is the slant height.

Given that the diameter is 8, the radius (r) is half of that, which is 8/2 = 4 units. To find the slant height (ℓ), we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (ℓ) is equal to the sum of the squares of the other two sides (radius and height).

Using the formula, we can calculate the slant height:

ℓ = √(r^2 + h^2)
= √(4^2 + 7^2)
= √(16 + 49)
= √65

Now, let's calculate the lateral surface area:

A = πrℓ
= π(4)(√65)

Using an approximation of π as 3.14, we can evaluate the expression:

A ≈ 3.14(4)(√65)
≈ 12.56(√65)

To find the base area of the cone, we use the formula for the area of a circle, A = πr^2:

Base Area = πr^2
= π(4^2)
= π(16)

Summing the lateral surface area and the base area, we get the total surface area of the cone:

Total Surface Area = Lateral Surface Area + Base Area
≈ 12.56(√65) + 16π

Therefore, the surface area of the given cone with a diameter of 8 units and a height of 7 units is approximately equal to 12.56(√65) + 16π.

To find the surface area of a cone, you need to know the slant height (l) and the radius (r) of the cone.

To find the slant height:
1. Use the Pythagorean theorem: l^2 = r^2 + h^2
- In this case, the height (h) is given as 7, and the diameter (d) is given as 8.
- The radius (r) can be calculated by dividing the diameter by 2: r = d/2 = 8/2 = 4.
- Substitute the values: l^2 = 4^2 + 7^2 = 16 + 49 = 65.
- Take the square root of both sides to find the slant height: l = √65 ≈ 8.06 (rounded to two decimal places).

To find the surface area:
2. The formula for the surface area of a cone is: A = πr(r + l)
- π is a mathematical constant (approximately equal to 3.14159).
- The radius (r) is 4, as calculated previously.
- The slant height (l) is approximately 8.06.
- Substitute the values into the formula: A = 3.14159 * 4(4 + 8.06).

Calculations:
- A = 3.14159 * 4(12.06)
- A = 3.14159 * 48.24
- A ≈ 151.90 square units.

Therefore, the surface area of the cone with a diameter of 8 and a height of 7 is approximately 151.90 square units.