Surface areas and volumes are important concepts in mathematics. They are used in various fields such as engineering, architecture, and construction. In this short note, we will discuss the formulas and figures of surface area and volume.

Surface Area Formulas:

The surface area of a solid is the total area that the surface of the solid covers. The formulas for surface area vary depending on the shape of the solid.

1. Cube: The surface area of a cube is given by 6a², where a is the length of the edge.

2. Cuboid: The surface area of a cuboid is given by 2(lw + lh + wh), where l, w, and h are the length, width, and height of the cuboid.

3. Cylinder: The surface area of a cylinder is given by 2πr² + 2πrh, where r is the radius and h is the height of the cylinder.

4. Sphere: The surface area of a sphere is given by 4πr², where r is the radius of the sphere.

Volume Formulas:

The volume of a solid is the amount of space that the solid occupies. Like surface area, the formulas for volume vary depending on the shape of the solid.

1. Cube: The volume of a cube is given by a³, where a is the length of the edge.

2. Cuboid: The volume of a cuboid is given by lwh, where l, w, and h are the length, width, and height of the cuboid.

3. Cylinder: The volume of a cylinder is given by πr²h, where r is the radius and h is the height of the cylinder.

4. Sphere: The volume of a sphere is given by 4/3πr³, where r is the radius of the sphere.

Figures:

The figures of the solid shapes help in understanding the formulas and how the measurements are taken. Below are the figures of the solid shapes mentioned above.

- Cube: A cube is a three-dimensional solid with six equal square faces.

- Cuboid: A cuboid is a three-dimensional solid with six rectangular faces.

- Cylinder: A cylinder is a three-dimensional solid with two circular faces and a curved surface.

- Sphere: A sphere is a three-dimensional solid with a perfectly round shape.

In conclusion, surface area and volume are essential concepts in mathematics, and their formulas and figures help in understanding the properties of different solid shapes.