There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
Solution:
The amount of material required to make boxes will be equal to their respective surface area.
Total surface area of the cuboid = Area of lateral surface + 2 × area of base = 2(lb + bh + hl) where, 'l', 'b' and 'h' are the length, breadth and height of the cuboid respectively.
Total surface area of the cube = 6(l)² where 'l' is the side of the cube
(a) l = 60cm, b = 40cm, h = 50cm
Total surface area of cuboid in the given figure = 2(lb + bh + hl)
= 2(60 × 40 + 40 × 50 + 60 × 50) cm²
= 2(2400 + 2000 + 3000) cm²
= 14800 cm²
(b) l = 50cm
Total surface area of cube in figure = 6 × (l)²
= 6 × (50)²
= 6 × 2500
= 15000 cm²
Thus, the cuboid box (a) requires a lesser amount of material as it has a lesser surface area.
☛ Check: NCERT Solutions for Class 8 Maths Chapter 11
Video Solution:
There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
Maths NCERT Solutions Class 8 Chapter 11 Exercise 11.3 Question 1
Summary:
There are two cuboidal boxes as shown in the adjoining figure. a) The total surface area of the cuboid is 14800 cm², b) The total surface area of the cube is 15000 cm². The cuboid box (a) requires a lesser amount of material as it has a lesser surface area.
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