"Question 2 A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Class 8 Mensuration Page 186"
Answers
Mensuration:
Mensuration is the branch of mathematics which concerns itself with the measurement of Lengths, areas & volume of different geometrical shapes or figures.
Surface area:
The surface area of a solid is the sum of the areas of the plane and curved faces of the solid.
It is measured in square units such as square centimetre (cm²) and square metre (m²).
Surface area of cuboid is the sum of the surface areas of its six rectangular faces.
Surface Area of Cuboid is =
2(lb + lh + bh)
By surface area of a cuboid we mean the total surface area.
The sum of the areas of 4 vertical faces of a cuboid is called its lateral surface area.
The lateral surface area or the area of the four walls of the cuboid .
Area of the four walls = 2 (l +b) h
==========================================================
Solution:
Given:
Length of suitcase box (l)= 80 cm
Breadth of suitcase box (b) = 48 cm
Height of cuboidal box=24 cm
Width of a trapaulin= 96 cm
Total Surface Area of Cuboid is
= 2(lb + lh + bh)
= 2 (80 x 48 + 80 x 24 + 48 x 24)
= 2(3840 + 1920 + 1152)
= 2 x 6912 = 13824
Surface area of one suitcase= 13824 cm²
Hence, Surface Area of 100 suitcases = 13824× 10
= 1382400 cm²
Area of tarpaulin cloth Required= surface
area of suitcase
L × B = 1382400
L × 96 = 1382400
L=1382400/96
L= 14400 cm
[ 1 cm = 1/100m]
L=144/100= 144 m
L= 144 m
Hence, 144 m of tarpaulin cloth is required to cover 100 suitcases.
==========================================================
Hope this will help you...