Cones, Pyramids, Spheres: Volume and Surface Area

The volume of a cone is given by the formula: $$V = \frac{1}{3} \pi r^2 h$$ , where r is the radius and h is the height.

The surface area of a sphere is given by the formula: $$A = 4 \pi r^2$$ , where r is the radius.

The volume of a pyramid is given by the formula: $$V = \frac{1}{3} B h$$ , where B is the area of the base and h is the height.

The radius is the distance from the center of a circle to any point on its circumference, while the diameter is twice the radius, extending from one point on the circumference to another through the center.

The surface area of a rectangular pyramid is calculated by adding the area of the base to the area of the triangular faces.

The volume of a sphere is given by the formula: $$V = \frac{4}{3} \pi r^3$$ , where r is the radius.

If the height of a cone is doubled, the volume also doubles, since volume is directly proportional to height.

The surface area of a cone is given by the formula: $$A = \pi r (r + l)$$ , where r is the radius and l is the slant height.

The diameter is always twice the radius: $$d = 2r$$ .

The volume of a square pyramid is calculated using the formula: $$V = \frac{1}{3} s^2 h$$ , where s is the length of a side of the base and h is the height.