Calculating Volumes of Various Shapes

Volume of Shapes

Cuboid Volumes

A cuboid is a rectangular prism with all edges parallel and opposite edges congruent. The volume of a cuboid is calculated by multiplying the area of the base (a rectangle) by the height (l). In mathematical notation, this can be represented as:

Volume = Base area × Height = alw

For example, if a cuboid has a base area of 9.5 cm², a height of 8 cm, and a volume of 1292 cm³, we can find the length (w) by solving the equation:

1292 = 9.5 × 8 × w

w = 1292 / (9.5 × 8) = 28 cm

Sphere Volumes

The volume of a sphere is given by the formula (4/3)πr³, where r is the radius of the sphere. For example, the volume of a sphere with a radius of 7 cm is (4/3)π(7³) = 336.28 cm³.

Composite Shapes

Composite shapes are made up of two or more regular solids. The volume of a composite shape can be found by adding the volumes of its constituent solids. For example, a composite prism with a base area of 9.5 cm² and a height of 8 cm has a volume of 9.5 × 8 = 76 cm³.

Cylinder Volumes

The volume of a cylinder is given by the formula πr²h, where r is the radius of the base and h is the height of the cylinder. For example, the volume of a cylinder with a base radius of 4 cm and a height of 7 cm is π(4²)7 = 98.21 cm³.

Prism Volumes

The volume of a prism is calculated by multiplying the area of the base (a rectangle) by the height of the prism. In mathematical notation, this can be represented as:

Volume = Base area × Height = alw

For example, if a prism has a base area of 9.5 cm², a height of 8 cm, and a volume of 1292 cm³, we can find the length (w) by solving the equation:

1292 = 9.5 × 8 × w

w = 1292 / (9.5 × 8) = 28 cm

Test your understanding of calculating volumes of different shapes, including cuboids, spheres, composite shapes, cylinders, and prisms. Practice applying formulas and solving problems to find the volume of various shapes.