Tricks to solve Volume and Surface Area Problems

  1. CUBOID
    Let 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. CUBE
    Let 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. CYLINDER
    Let 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. CONE
    Let 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. SPHERE
    Let the radius of the sphere be r. Then,

    1. Volume = r3 cubic units.
    2. Surface area = (4r2) sq. units.
  6. HEMISPHERE
    Let 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:
      A. 12 cm3
      B. 15 cm3
      C. 16 cm3
      D. 20 cm3

      Answer: Option A

      Explanation:

      Clearly, we have r = 3 cm and h = 4 cm.

       Volume = 1 r2h = 1  x 32 x 4 cm3 = 12 cm3.
      3 3
      In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
      A. 75 cu. m
      B. 750 cu. m
      C. 7500 cu. m
      D. 75000 cu. m

      Answer: Option B

      Explanation:

      1 hectare = 10,000 m2

      So, Area = (1.5 x 10000) m2 = 15000 m2.

      Depth = 5 m = 1 m.
      100 20
       Volume = (Area x Depth) = 15000 x 1 m3 = 750 m3.
      20

      A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

      66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

      A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:

      A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

      50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

Don't miss out!
Subscribe To Our Newsletter

Learn new things. Get an article everyday.

Invalid email address
Give it a try. You can unsubscribe at any time.

Leave a Reply

Your email address will not be published. Required fields are marked *