Surface area of a square pyramid
11in 13in and 9in
11 height
13 side?
9 base edge
I keep getting the wrong answer its not 328.62 or 294.93
Square area of a cone
15 side?
12 height
6 base
It's not 365.99 or 417.62
I don't need anything rounded...help please!
If 13 is the slant height of a triangular face, then the area of the pyramid is just the base plus four triangles:
11*11 + 4*(11*13/2) = 407
I keep having trouble guessing what you mean by "side" especially of a cone.
To find the surface area of a square pyramid, you need to calculate the sum of the areas of all its faces. A square pyramid has 4 triangular faces and 1 square base.
First, let's calculate the area of each face:
1. Base Area:
The base of the square pyramid is a square, so the area is given by the formula A = side^2. In this case, the base edge is 9 inches, so the area of the base is A = 9^2 = 81 square inches.
2. Lateral Faces:
The four triangular lateral faces all have the same dimensions. To find the area of a triangle, you can use the formula: A = (1/2) * base * height. In this case, the base of each triangular face is 13 inches and the height is 11 inches. So the area of each lateral face is A = (1/2) * 13 * 11 = 71.5 square inches.
To calculate the surface area of the square pyramid, add the areas of the base and the four lateral faces:
Surface Area = Base Area + 4 * Lateral Face Area
Surface Area = 81 + 4 * 71.5
Surface Area = 81 + 286
Surface Area = 367 square inches (without rounding)
Therefore, the surface area of the given square pyramid is 367 square inches.
For the square cone:
To calculate the surface area of a square cone, we need to find the area of the square base and the lateral curved surface area.
1. Base Area:
The base of the square cone is a square, so the area is given by the formula A = side^2. In this case, the side of the base is 6 inches, so the area of the base is A = 6^2 = 36 square inches.
2. Curved Surface Area:
The curved surface area of a cone is given by the formula A = π * r * l, where r is the radius of the base and l is the slant height. In this case, the side of the cone is 15 inches, which corresponds to the slant height. To find the radius, we divide the side length by √2 (approximately 1.414). So, the radius is 15 / 1.414 = 10.606 inches.
Now, we can calculate the curved surface area as A = π * r * l = π * 10.606 * 15 = 500.445 square inches.
To find the surface area of the square cone, add the area of the base and the curved surface area:
Surface Area = Base Area + Curved Surface Area
Surface Area = 36 + 500.445
Surface Area = 536.445 square inches (without rounding)
Therefore, the surface area of the given square cone is approximately 536.445 square inches.