Class 9 Mathematic Surface Areas and Volumes All Formula & Concept Notes | Formula Sheet

I can provide a detailed overview of the formulas and concepts for Surface Areas and Volumes in Class 9 Mathematics. This topic typically covers the surface areas and volumes of various solid figures such as cubes, cuboids, spheres, cylinders, and cones. Here’s a breakdown:

1. Cube

• Surface Area: The surface area of a cube is the total area of all six faces.

  $$\text{Surface Area} = 6a^2$$

  where $a$ is the length of an edge.

• Volume: The volume of a cube is the amount of space enclosed within it.

  $$\text{Volume} = a^3$$

  where $a$ is the length of an edge.

2. Cuboid

• Surface Area: The surface area of a cuboid is the sum of the areas of all six faces.

  $$\text{Surface Area} = 2(lb + bh + lh)$$

  where $l$ is the length, $b$ is the breadth, and $h$ is the height.

• Volume: The volume of a cuboid is the amount of space enclosed within it.

  $$\text{Volume} = l \times b \times h$$

  where $l$, $b$, and $h$ are the length, breadth, and height, respectively.

3. Sphere

• Surface Area: The surface area of a sphere is the total area of its curved surface.

  $$\text{Surface Area} = 4\pi r^2$$

  where $r$ is the radius.

• Volume: The volume of a sphere is the amount of space enclosed within it.

  $$\text{Volume} = \frac{4}{3}\pi r^3$$

  where $r$ is the radius.

4. Cylinder

• Surface Area: The surface area of a cylinder includes the area of the two circular bases and the rectangular side.

  $$\text{Surface Area} = 2\pi r(h + r)$$

  where $r$ is the radius of the base and $h$ is the height.

• Volume: The volume of a cylinder is the amount of space enclosed within it.

  $$\text{Volume} = \pi r^2 h$$

  where $r$ is the radius of the base and $h$ is the height.

5. Cone

• Surface Area: The surface area of a cone includes the area of the base and the lateral surface area.

  $$\text{Surface Area} = \pi r (r + l)$$

  where $r$ is the radius of the base and $l$ is the slant height.

• Volume: The volume of a cone is the amount of space enclosed within it.

  $$\text{Volume} = \frac{1}{3} \pi r^2 h$$

  where $r$ is the radius of the base and $h$ is the height.

6. Hemisphere

• Surface Area: The surface area of a hemisphere includes the curved surface area and the area of the base.

  $$\text{Surface Area} = 3\pi r^2$$

  where $r$ is the radius.

• Volume: The volume of a hemisphere is half the volume of a sphere.

  $$\text{Volume} = \frac{2}{3} \pi r^3$$

  where $r$ is the radius.

These formulas and concepts form the basis for solving problems related to surface areas and volumes in Class 9 Mathematics.