WORD PROBLEMS RELATED TO
MENSURATION
CLASS 8th, 9th & 10th
Q.1) A cuboid has a total surface area of 160 sq. m and lateral surface area of 120 sq. m. Find the area of it’s base ?
SOLUTION : Cuboid
Given : Total surface area =TSA = 160 sq. m.
Lateral surface area = LSA = 120 sq. m.
Find the area of it’s base = ?
Area of it’s base = L* B = ?
Step 1) : LSA = 2( b*h + h*l )
120 = 2 ( b*h + h*l )
120/2 = ( b*h + h*l)
60m = (b*h + h*l)
Step 2) : TSA = 2 ( l*b + b*h + h*l )
160 = 2 ( l*b + 60 ) (Substituting step 1 in step 2)
160/2 = l*b +60
80 – 60 = l*b
20 = l*b
20 sq. m = l*b = Area of it’s base.
Q.2 ) If the total surface area of a cubical box is 864 sq. cm. Find the edge of the cube?
SOLUTION : Cubical box
Given : Total surface area = TSA = 864 sq. m.
Find the edge of the cube = a =?
TSA = 6*a*a
864 = 6 *a*a
864/6= a*a
144 = a*a
12*12 =a*a
12 cm. = a = edge of the cube.
Q.3) If the edge of the cube is trebled, what will be the change in it’s surface area ?
SOLUTION : Cube
Given : edge = a units
Step 1 ) Total surface area = TSA = 6 * a*a units
Step 2) If the edge is trebled , edge = 3a units
TSA = 6 * 3a *3a = 54a*a units.
Hence if the edge is trebled then the TSA will increase 9 times i.e. it will increase by 48a*a units.
Q.4) Five cubes of sides 6m each are placed side and stuck together to form a cuboid. If the outer surface is to be painted at Rs.3 per sq m ,find the total cost of painting?
SOLUTION :
Given : No. of cubes = 5
side of cube = 6m
5 cubes stuck together to form a cuboid.
find the total surface area of cuboid= TSA = ?
Rate of painting = Rs.3per sq m.
Step 1). Cuboid
Length =L = 6*5 = 30 m.
Breadth = B= 6m.
Heigth =H =6m.
TSA= 2( l*b + b*h + h*l )
= 2 ( 30*6 + 6*6 + 6*30 )
= 2 (180 + 36 + 180 )
= 2 * 396
= 792 sq m.
Step 2). Total cost = TSA *rate
= 792 * 3 = Rs. 2376
Ans : The total cost of painting is Rs. 2376
Q.5)A seven meter long cylindrical wire has a radius of 8mm. Find the curved surface area of the
wire ?
SOLUTION : Cylindrical wire
Given : Length = heigth = h= 7m = 7 * 1000 = 7000mm.
Radius 8mm.
Find the curved surface area = lateral surface area= LSA=?
LSA =2*pie * r*h
=2* 22/7*8*7000
= 352000 sq mm.
= 352000/1000000 (1 sq mm = 1000000 sq m.)
= 0.352 sq m.
Ans. The curved surface area is 0.352 sq m.