## Aptitude Volume and Surface Area Concepts and formulas1) Let length = l, breadth = b, and height = h units - Volume of cuboid = (l x b x h) cubic units
- Whole surface area of cuboid = 2 (lb + bh +hl) sq. units.
- Diagonal of cuboid = units.
2) Let each edge of a cube = "a" units. Then: - Volume of the cube = a
^{3}cubic units. - Whole surface area of cube = (6a
^{2}) sq. units. - Diagonal of the cube
3) Let the radius of the base of a cylinder be r units and height of the cylinder be h units. Then: - Volume of the cylinder = (πr
^{2}h) cubic units. - Curved surface area of the cylinder = (2πrh) sq. units.
- Total surface area of the cylinder =(2πrh+2πr
^{2}) sq. units.
4) Let r be the radius of the sphere. Then: - Volume of the sphere = cubic units.
- Surface area of the sphere sq. units.
- Volume of hemisphere cubic units.
- Curved surface area of the hemisphere = (2 πr
^{2}) sq. units. - Whole surface area of the hemisphere = (3 πr
^{2}) sq. units.
5) Let r be the radius of the base, h is the height, and l is the slant height of the cone. Then: - Slant height l
- Volume of the cone cubic units.
- Curved surface area of the cone = (πrl) sq. units sq. units.
- Total surface area of the cone = (πrl+ πr
^{2})= πr(l+r) sq.units.
6) Let the radius of the base of the frustum = R, the radius of top = r, height = h and slant height = l units. - Slant height,
- Curved surface area = π (r + R) l sq. units.
- Total surface area = π { (r + R) l + r
^{2}+ R^{2}} sq. units. - Volume cubic units.
## Some Quicker methods:
- Capacity = (external length - 2 x thickness) x (external breadth - 2 x thickness) x (external height - 2 x thickness)
- Volume of material = External volume - capacity
- Weight of wood = Volume of wood x density of wood.
(i) (Ratio of radii) (ii) Ratio of volumes = (ratio of radii) (iii) (Ratio of surface areas)
(i) Ratio of volumes = ratio of heights. (ii) Ratio of curved surface areas = ratio of heights (iii) Ratio of volumes = (ratio of curved surface areas)
(i) Ratio of volumes = (ratio of radii) (ii) Ratio of curved surface areas = ratio of radii (iii) Ratio of volumes = (ratio of curved surface areas)
(i) Ratio of radii (ii) Ratio of curved surface areas
(i) Ratio of volumes = ratio of radii (ii) Ratio of volumes = inverse ratio of heights. (iii) Ratio of radii = inverse ratio of heights. Aptitude Volume and Surface Area Test Paper 1 Aptitude Volume and Surface Area Test Paper 2 Aptitude Volume and Surface Area Test Paper 3 Aptitude Volume and Surface Area Test Paper 4 Aptitude Volume and Surface Area Test Paper 5 |

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