Volume Of A Combination Of Solids

A solid which is bounded by six rectangular faces is known as cuboid and if the length, breadth and height of the cuboid are equal, then it is a cube.

8 vertices, 6 faces and 12 edges are there in both cube and cuboid. Base of the cuboid is any face of the cuboid.

For a cuboid which has length (l), breadth (b) and height (h) has:

  • Volume = l×b×h
  • Total surface area = 2(lb+bh+lh)

For a cube with length x,

  • Volume = x3 (because l = b = h = x)
  • Total surface area = 6x2

Solved Examples

Q1. For a room of dimension 10 m × 8 m × 9 m. Find out the longest pole that can be put in this room.

Solution: Longest pole is the longest diagonal of the room= √(102+92+82)

= √245

= 15.652 m

The longest pole that can be put inside the room has length = 15.652 m.

Q2. A cube has a volume 343 cm3.Find the surface area of the cube.

Solution: The volume of the cube=a3=343

a = 3√343 = 7

Total surface area=6a2

=6×72= 294 cm2

Total surface area of the cube = 294 cm2

Q.3. A cuboidal water tank is aluminium steel sheet which is 4.5 m thick. The outer dimensions are 1.5 m × 2.5 m × 3 m. Find the internal dimensions and total surface area of the tank.

Solution: External dimensions of the cube are:

l = 150 cm, b = 250 cm and h = 300 cm

As we know that the sheet is 4.5 m thick, the internal dimensions are:

L = (150-9) cm = 141 cm

B=(250-9) = 241 cm

H= (300-9) = 291 cm

Total surface area of the tank = 2(lb + bh + lh)

= 2(1.5×2.5+2.5×3+3×1.5)

= 31.5 m3.

Q.4. How many tissue boxes of size 10 cm × 8 cm × 9 cm can be adjusted inside a cupboard box of size 36 cm × 40 cm × 100 cm.

Solution: Volume of the tissue box = 10 x 8 x 9 cm3

= 720 cm3

Volume of the cupboard = 36 x 40 x 100 cm3.

= 144,000 cm3

Combination Of Solids

=200 boxes

Therefore, we can say that 200 tissue boxes can be adjusted in the cupboard box. For more information contact BYJU’S mentors.

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