Find the surface area of the cone. Use 3.14 for pi. The radius is 8in and the height is 7in please help asap!! And thank you for your time. Ms.Sue?
A=πr(r+√[h^2+r^2])
Insert values and solve.
thx psyDAGGGGGGGGGGGGG
To find the surface area of a cone, we need to calculate the lateral surface area and the base area separately, and then add them together.
1. Lateral Surface Area:
The formula for the lateral surface area of a cone is A = πrℓ, where A is the lateral surface area, r is the radius of the base, and ℓ is the slant height (the distance from the tip of the cone to a point on its circumference).
To find the slant height, we can use the Pythagorean theorem. The slant height, ℓ, can be calculated as:
ℓ = √(r^2 + h^2)
Given the radius, r = 8in, and the height, h = 7in, we can substitute these values into the formula:
ℓ = √(8^2 + 7^2)
ℓ = √(64 + 49)
ℓ = √113
ℓ ≈ 10.63in
Now, we can calculate the lateral surface area:
A = π * r * ℓ
A = 3.14 * 8 * 10.63
A ≈ 266.56 sq.in.
2. Base Area:
The base area of a cone is given by the formula A = πr^2, where A is the base area and r is the radius.
Substituting the given radius into the formula, we get:
A = 3.14 * 8^2
A = 3.14 * 64
A ≈ 201.06 sq.in.
3. Total Surface Area:
To find the total surface area, we add the lateral surface area and the base area together:
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area ≈ 266.56 + 201.06
Total Surface Area ≈ 467.62 sq.in.
So, the surface area of the cone is approximately 467.62 square inches.
To find the surface area of a cone, you need to find the sum of the lateral surface area and the base area.
1. Lateral Surface Area:
The lateral surface area of a cone can be calculated using the formula: LSA = π * r * l, where r is the radius of the base and l is the slant height of the cone.
To find the slant height, you can use the Pythagorean theorem. The slant height (l) is the hypotenuse of a right triangle formed by the height (h) and the radius (r) of the cone. So, l = sqrt(r^2 + h^2).
Given:
Radius (r) = 8 inches
Height (h) = 7 inches
First, find the slant height:
l = sqrt(r^2 + h^2)
l = sqrt(8^2 + 7^2)
l = sqrt(64 + 49)
l = sqrt(113)
l ≈ 10.63 inches (rounded to two decimal places)
Now, calculate the lateral surface area:
LSA = π * r * l
LSA = 3.14 * 8 * 10.63
LSA ≈ 267.94 square inches (rounded to two decimal places)
2. Base Area:
The base area of a cone is given by the formula: Base Area = π * r^2.
Given:
Radius (r) = 8 inches
Base Area = π * r^2
Base Area = 3.14 * 8^2
Base Area ≈ 201.06 square inches (rounded to two decimal places)
3. Total Surface Area:
The surface area of a cone is the sum of the lateral surface area and the base area.
Total Surface Area = Lateral Surface Area + Base Area
Total Surface Area = 267.94 + 201.06
Total Surface Area ≈ 469 square inches (rounded to two decimal places)
So, the surface area of the cone is approximately 469 square inches.