Surface Area

Surface area is the total area that the surface of a three-dimensional object occupies.

The surface area of a cube is given by the formula: $$6a^2$$ , where $$a$$ is the length of a side.

The surface area of a cylinder is given by the formula: $$2\text{π}r(h + r)$$ , where $$r$$ is the radius and $$h$$ is the height.

The surface area of a sphere is given by the formula: $$4\text{π}r^2$$ , where $$r$$ is the radius.

A net is a two-dimensional representation of a three-dimensional shape that can be folded to form the shape.

The vertical cross-section of a cylinder is a rectangle.

To calculate the surface area of a prism, find the area of the base and multiply by the height, then add the areas of the lateral faces.

The surface area of a square pyramid is given by the formula: $$\frac{1}{2}pl + b$$ , where $$p$$ is the perimeter of the base, $$l$$ is the slant height, and $$b$$ is the area of the base.

The lateral surface area of a cylinder is given by the formula: $$2\text{π}rh$$ , where $$r$$ is the radius and $$h$$ is the height.

The surface area is $$2\text{π}(3)(5) + 2\text{π}(3)^2 = 30\text{π} + 18\text{π} = 48\text{π} \text{ in}^2$$ .