W0RD PROBLEMS RELATED TO
MENSURATION
CLASS 8TH, 9TH & 10TH
Formulas :-
1). Cube:
Total surface area = TSA = 6a2
Lateral surface area = LSA = 4a2
Volume = V = a2
2). CUBOID:
Total surface area = TSA = 2 (l*b + b*h + h*l)
Lateral surface area = LSA = 2(b*h + h*l)
Volume = v = l*b*h
3). Cylinder:
Total surface area = TSA = 2*pie*r(h + r)
Lateral surface area = LSA = 2*pie*r*h
Volume = pie*r2*h
Q.1) If the total surface area of a cube is 3750 cm2, find its volume?
SOLUTION : CUBE
Given : Total surface area = TSA = 3750 cm2
Find : Volume ?
Step 1) TSA = 6*a2
3750 = 6 a2
3750/6 = a2
625 = a2
25cm=a
Step 2) Volume = a3
V = (25)3
V = 15625 cm3
Ans: Volume of cube is 15625 cm3
Q.2). The area of the floor of a room is 85.5 m2 . Its volume is 983.25m3. Find the height of the
room?
SOLUTION: Room (cuboid) 3
Given : Area of the floor = 85.5m2 = L *B
Volume = 983.25m3
Height = ?
Volume = L*B*H
983.25 = 85.5 * H
983.25/85.5 = H
11.5 m = H
Ans : The height of the room is 11.5 m.
Q.3) The diameter of the base of a right circular cylinder is 42cm and its height is 12cm. Find
its volume?
SOLUTION: Right circular cylinder
Given : diameter =d = 42cm radius = r= 42/2 = 21cm.
height = h = 12 cm.
Find: volume = ?
volume = pie * r2 * h
v = 22/7 *21*21*12
= 16,632cm2
Ans : The volume is 16,632cm
Q.4) How many cuboidal match boxes of dimensions 8cm x 6cm x 2cm can be placed in a
cubical packing with edge 24cm ?
SOLUTION:
Step 1 : Cuboidal boxes
L = 8cm , B = 6cm , H = 2cm
Find Number (N) of cuboidal boxes = ?
Volume of cuboidal box = L * B * H
=8 * 6 * 2
= 96 cm 3
Step 2 : Cubical packing
edge = a = 24cm
volume of cubical packing = a3
= (24)3 cm
=13824cm3
Step 3 : N of cuboidal boxes = Volume of cubical boxes / Volume of cuboidal box
= 13824 / 96
Ans : N of cuboidal boxes = 144 boxes
Q 5 ). There is a big ice cream brick with dimensions 24cm x 15cm x 8cm to be distributed among family members . If each member gets 240cm3 of ice cream to eat , find the number of family members .
SOLUTION:
Ice cream Brick ( cuboidal)
Given : – L = 24cm , B = 15cm , H = 8cm
Volume of ice cream brick = L x B x H = 24 x 15 x 8 = 2880cm3
Volume of ice cream each member gets = 240 cm3
Find number of family members = ?
Number of family members = Volume of cuboidal ice cream brick / volume of ice cream each member gets
= 2880 / 240 = 12 members = Ans