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 as well as 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
Volume of combination of solids Examples:
Q1. For a room of dimension 10m×8m×9m.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)
The longest pole that can be put inside the room has length=15.652m.
Q2. A cube has a volume 343cm3.Find the surface area of the cube.
Solution: The volume of the cube=a3=343
a = 3√343 = 7
Total surface area=6a2
Total surface area of the cube=294cm2
Q.3. A cuboidal water tank is aluminium steel sheet which is 4.5m thick. The outer dimensions are 1.5m×2.5m×3m. Find the internal dimensions and total surface area of the tank.
Solution: External dimensions of the cube are:
l=150cm, b=250cm and h=300cm.
As we know that the sheet is 4.5m thick, the internal dimensions are:
H= (300-9) =291cm
Total surface area of the tank=2(lb+bh+lh)
Q.4. How many tissue boxes of size 10cm×8cm×9cm can be adjusted inside a cupboard box of size 36cm×40cm×100cm.
Solution: Volume of the tissue box = 10 x 8 x 9 cm3
Volume of the cupboard = 36 x 40 x 100 cm3.
Therefore we can say that 200 tissue boxes can be adjusted in the cupboard box. For more information contact byju’s mentors.