Surface Areas and Volumes
Surface Area is the area of the outer part of any 3D figure and Volume is the capacity of the figure i.e. the space inside the solid. To find the surface areas and volumes of the combination of solids, we must know the surface area and volume of the solids separately. Some of the formulas of solids are –
| Name | Figure | Lateral or Curved Surface Area | Total Surface Area | Volume | Length of diagonal and nomenclature |
| Cube | 4l2 | 6l2 | l3 | √3l = edge of the cube | |
| Cuboid | 2h(l +b) | 2(lb + bh + hl) | lbh | l = lengthb = breadthh = height | |
| Cylinder | 2πrh | 2πr2 + 2πh = 2πr(r + h) | πr2h | r = radiush = height | |
| Hollow cylinder | 2πh (R + r) | 2πh (R + r) + 2πh (R2 – r2) | – | R = outer radiusr = inner radius | |
| Cone | πl=π√h2+r2 | πr2 + πrl = πr(r + l) | (1/3)πr2h | r = radiush = heightl = slant height | |
| Sphere | 4πr2 | 4πr2 | (4/3)πr3 | r = radius | |
| Hemisphere | 2πr2 | 3πr2 | (2/3) πr3 | r = radius | |
| Spherical shell | 4πR2 (Surface area of outer) | 4πr2 (Surface area of outer) | 4/3 π(R3 – r3) | R = outer radiusr = inner radius | |
| Prism | Perimeter of base × height | Lateteral surface area + 2(Area of the end surface) | Area of base × height | – | |
| pyramid | 1/2 (Perimeter of base) × slant height | Lateral surface area + Area of the base | 1/3 area of base × height | – |
Surface Area of a Combination of Solids
If a solid is molded by two or more than two solids then we need to divide it in separate solids to calculate its surface area.
Frustum of a Cone
If we cut the cone with a plane which is parallel to its base and remove the cone then the remaining piece will be the Frustum of a Cone.
| Volume of the frustum of the cone | |
| The curved or Lateral surface area of the frustum of the cone | |
| Total surface area of the frustum of the cone | Area of the base + Area of the top + Lateral surface area |
| Slant height of the frustum |