Volume (Cylinders, Cones, Spheres)

Volume is the amount of space it takes to fill the inside of a 3D object.

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

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

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

Common units of volume include cubic centimeters (cm³), cubic meters (m³), liters (L), and gallons.

Using the formula $$V = \text{π}r^2h$$ , the volume is $$V = \text{π}(3^2)(10) = 90\text{π} \text{ cm}^3$$ .

The radius and height of a cone are independent dimensions; however, they both affect the volume of the cone.

The label 'yd²' (square yards) is NOT a correct label for volume; volume is measured in cubic units.

True, the radius and height of a cylinder can be equal, but they do not have to be.

Using the formula $$V = \frac{4}{3} \text{π}r^3$$ , the volume is $$V = \frac{4}{3} \text{π}(2.2)^3 \text{ cm}^3$$ .