Surface Area and Volumes of 3D Shapes: Sphere, Cuboid, Cone, and Pyramid

6 Questions

What is the formula for the surface area of a sphere?

4πr²

Calculate the volume of a sphere with radius 5 units.

(4/3)π(5)³

How is the surface area of a cuboid calculated?

2lh + 2lb + lb

Find the volume of a cuboid with dimensions 4 units by 3 units by 6 units.

4(3)(6)

What is the formula for the curved surface area of a cone?

(1/2)rl

Calculate the volume of a cone with radius 8 units and height 10 units.

(1/3)π(8)²(10)

Study Notes

Surface Area and Volumes of 3D Shapes: Sphere, Cuboid, Cone, and Pyramid

The surface area and volume of 3D shapes are crucial concepts in mathematics and physics. Understanding these properties allows us to calculate various quantities, such as the amount of paint needed to cover a surface or the volume of materials required for a project. In this article, we will discuss the surface area and volumes of three common 3D shapes: sphere, cuboid, cone, and pyramid.

Sphere

A sphere is a three-dimensional shape with all points equidistant from its center. The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere. The volume of a sphere is calculated using the formula (4/3)πr³.

Cuboid

A cuboid is a rectangular prism with six square faces. The surface area of a cuboid is calculated by adding the area of all its six faces. For a cuboid with length l, breadth b, and height h, the total surface area is given by the formula 2lh + 2lb + lb. The volume of a cuboid is calculated by multiplying its length, breadth, and height, resulting in the formula lbh.

Cone

A cone is a pyramid with a circular base. The surface area of a cone includes the area of the base and the curved surface area. The formula for the curved surface area of a cone is given by the formula (1/2)rl, where r is the radius of the base and l is the height of the cone. The volume of a cone is calculated using the formula (1/3)πr²h.

Pyramid

A pyramid is a three-dimensional shape with a polygonal base and triangular faces that connect to the base. The volume of a pyramid is given by the formula (1/3)Area of Base × Vertical Height. For example, a pyramid with a square base of side length s and height h will have a volume of (1/3)s²h.

In summary, understanding the surface area and volumes of various 3D shapes is essential in mathematics and physics. By knowing these formulas, we can calculate the total surface area and volume of different shapes, which can be useful in real-life situations, such as determining the amount of paint needed to cover a surface or calculating the volume of materials required for a project.