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Aptitude Volume and Surface Area Concepts and formulas

1) Cuboid:

Let length = l, breadth = b, and height = h units

  1. Volume of cuboid = (l x b x h) cubic units
  2. Whole surface area of cuboid = 2 (lb + bh +hl) sq. units.
  3. Diagonal of cuboid = Apti Volume and Surface Area units.

2) Cube:

Let each edge of a cube = "a" units. Then:

  1. Volume of the cube = a3 cubic units.
  2. Whole surface area of cube = (6a2) sq. units.
  3. Diagonal of the cube Apti Volume and Surface Area

3) Cylinder:

Let the radius of the base of a cylinder be r units and height of the cylinder be h units. Then:

  1. Volume of the cylinder = (πr2 h) cubic units.
  2. Curved surface area of the cylinder = (2πrh) sq. units.
  3. Total surface area of the cylinder =(2πrh+2πr2) sq. units.

4) Sphere:

Let r be the radius of the sphere. Then:

  1. Volume of the sphere = Apti Volume and Surface Area cubic units.
  2. Surface area of the sphere Apti Volume and Surface Area sq. units.
  3. Volume of hemisphere Apti Volume and Surface Area cubic units.
  4. Curved surface area of the hemisphere = (2 πr2) sq. units.
  5. Whole surface area of the hemisphere = (3 πr2) sq. units.

5) Right circular cone:

Let r be the radius of the base, h is the height, and l is the slant height of the cone. Then:

  1. Slant height l Apti Volume and Surface Area
  2. Volume of the cone Apti Volume and Surface Area cubic units.
  3. Curved surface area of the cone = (πrl) sq. units Apti Volume and Surface Areasq. units.
  4. Total surface area of the cone = (πrl+ πr2 )= πr(l+r) sq.units.

6) Frustum of a right circular cone:

Let the radius of the base of the frustum = R, the radius of top = r, height = h and slant height = l units.

  1. Slant height, Apti Volume and Surface Area
  2. Curved surface area = π (r + R) l sq. units.
  3. Total surface area = π { (r + R) l + r2 + R2 } sq. units.
  4. Volume Apti Volume and Surface Area cubic units.

Some Quicker methods:

1) For a closed wooden box:

  1. Capacity = (external length - 2 x thickness) x (external breadth - 2 x thickness) x (external height - 2 x thickness)
  2. Volume of material = External volume - capacity
  3. Weight of wood = Volume of wood x density of wood.

2) Problems involving ratios:

I. Two Spheres:

(i) (Ratio of radii)2 = ratio of surface areas.

(ii) Ratio of volumes = (ratio of radii)3

(iii) (Ratio of surface areas)3 = (ratio of volumes)2

II. Two cylinders:

a. When the radii are equal:

(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)

b. When heights are equal

(i) Ratio of volumes = (ratio of radii)2

(ii) Ratio of curved surface areas = ratio of radii

(iii) Ratio of volumes = (ratio of curved surface areas)2

c. When volumes are equal

(i) Ratio of radiiApti Volume and Surface Area

(ii) Ratio of curved surface areas Apti Volume and Surface Area

d. When curved surface areas are equal

(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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