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