Volume and Surface Area of Solids

The volume V of a cylinder is given by the formula: V = $$\text{π}r^2h$$ , where r is the radius and h is the height.

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

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

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

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

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

Using the formula V = $$\text{π}r^2h$$ , the volume is V = $$\text{π}(3)^2(5) = 45\text{π} \text{ cm}^3$$ .

Using the formula V = $$\frac{1}{3}\text{π}r^2h$$ , the volume is V = $$\frac{1}{3}\text{π}(4)^2(9) = 48\text{π} \text{ in}^3$$ .

The diameter d of a circle is twice the radius r: d = 2r.

Volume measures the amount of space inside a solid, while surface area measures the total area of the surface of the solid.