6 Questions
What is the formula for the volume of a sphere?
(4/3)πr³
What is the formula for the volume of a cylinder?
πr²h
What is the formula for the volume of a prism?
Base area × Height
What is the formula for the volume of a cuboid?
alw
How do you find the volume of a composite shape?
By adding the volumes of its constituent solids
What is the length of a cuboid with a base area of 9.5 cm², a height of 8 cm, and a volume of 1292 cm³?
28 cm
Study Notes
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.
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