CLASS-7
SURFACE AREA AND VOLUME OF SOLIDS

SURFACE AREA AND VOLUME OF SOLIDS -

The surface area and volume of solids are fundamental concepts in geometry. They are used to determine the amount of space a solid occupies (volume) and the extent of its surface (surface area). Here's a breakdown of the formulas for different common solids:

1. Cube:-

• Surface Area:- The total area of all six square faces.

                           A = 6a²

                       Where a is the length of a side.             

• Volume:- The amount of space enclosed by the cube.

                           V = a³

2. Rectangular Prism (Cuboid):-

• Surface Area:- The sum of the areas of all six rectangular faces.

                        A = 2lw + 2lh + 2wh

         Where l, w, and h are the length, width, and height, respectively.

• Volume:- The space occupied by the rectangular prism.

                              V = lwh

3. Sphere:-

• Surface Area:- The area of the spherical surface.

                                  A = 4πr² 

                         Where r is the radius.

• Volume:- The space enclosed by the sphere.

                                 V = 4/3πr³

4. Cylinder:-

• Surface Area:- The area of the two circular bases and the rectangular side (lateral surface).

                                 A = 2πr² + 2πrh

                    Where r is the radius of the base and h is the height.

• Volume:- The space enclosed by the cylinder.

                                  V = πr²h

5. Cone:-

• Surface Area:- The area of the base and the lateral surface.

                             A = πr²+ πr √(r²+h²)

              Where r is the radius of the base and h is the height.

• Volume:- The space enclosed by the cone.

                            V = 1/3πr²h

6. Pyramid:-

• Surface Area:- The area of the base and the lateral faces.

                          A = B + 1/2 Pl

       Where B is the area of the base, P is the perimeter of the base, and l is the slant height.

• Volume:- The space enclosed by the pyramid.

                           V = 1/3 Bh

       Where h is the vertical height from the base to the apex.

7. Torus:-

• Surface Area:- The area of the surface of the donut-shaped solid.

                         A = 4π²Rr

       Where R is the distance from the center of the tube to the center of the torus and r is the radius of the tube.

• Volume:- The space enclosed by the torus.

                        V = 2π²Rr²

These formulas are essential for solving problems involving three-dimensional objects.