Volume And Surface Area- Simple Formulae

  1. CUBOIDLet length = l, breadth = b and height = h units. Then
    1. Volume = (l x b x h) cubic units.
    2. Surface area = 2(lb + bh + lh) sq. units.
    3. Diagonal = l2 + b2 + h2 units.
  2. CUBELet each edge of a cube be of length a. Then,
    1. Volume = a3 cubic units.
    2. Surface area = 6a2 sq. units.
    3. Diagonal = 3a units.
  3. CYLINDERLet radius of base = r and Height (or length) = h. Then,
    1. Volume = (r2h) cubic units.
    2. Curved surface area = (2rh) sq. units.
    3. Total surface area = 2r(h + r) sq. units.
  4. CONELet radius of base = r and Height = h. Then,
    1. Slant height, l = h2 + r2 units.
    2. Volume = r2h cubic units.
    3. Curved surface area = (rl) sq. units.
    4. Total surface area = (rl + r2) sq. units.
  5. SPHERELet the radius of the sphere be r. Then,
    1. Volume = r3 cubic units.
    2. Surface area = (4r2) sq. units.
  6. HEMISPHERELet the radius of a hemisphere be r. Then,
    1. Volume = r3 cubic units.
    2. Curved surface area = (2r2) sq. units.
    3. Total surface area = (3r2) sq. units.Note: 1 litre = 1000 cm3.

      A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

      The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

      A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

      The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

      15. How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

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