Final answer:
To find the surface area of a pyramid, you calculate the area of the base and the area of the lateral faces using formulas.
The formula for the surface area of a pyramid is A = B + (1/2)Pl, where A is the surface area, B is the area of the base, P is the perimeter of the base, and l is the slant height.
The formula for the surface area of a cylinder is A = 2πr^2 + 2πrh, where A is the surface area, r is the radius of the base, and h is the height of the cylinder.
Step-by-step explanation:
To find the surface area of a pyramid, you need to find the area of the base and the area of the lateral faces. The formula for the surface area of a pyramid is A = B + (1/2)Pl, where A is the surface area, B is the area of the base, P is the perimeter of the base, and l is the slant height of the pyramid.
Given that the height of the pyramid is 6 and the base is 8, we can find the area of the base using the formula for the area of a rectangle, which is A = length x width. So, the area of the base of the pyramid is A = 8 x 8 = 64 square units.
To find the slant height, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the height is the perpendicular side, the base is the base side, and the slant height is the hypotenuse. So, using the Pythagorean theorem, we can find the slant height as l = square root(8^2 + 6^2) = square root(100) = 10.
Now we can calculate the surface area of the pyramid as A = 64 + (1/2)(P)(l) = 64 + (1/2)(8)(10) = 64 + 40 = 104 square units.
To find the surface area of a cylinder, you need to find the areas of the two circular bases and the lateral surface area. The formula for the surface area of a cylinder is A = 2πr^2 + 2πrh, where A is the surface area, r is the radius of the base, and h is the height of the cylinder.
Given that the radius of the cylinder is 3 and the length is 5, we can calculate the surface area as A = 2π(3)^2 + 2π(3)(5) = 18π + 30π = 48π square units.