Important Questions for Class 8 Maths - Mensuration

Q1: Match the column.
Ans:
(p) → (iv)
(q) → (i)
(r) → (ii)
(s) → (iii)

Q2: Fill in the blanks
(i) Curved surface area of a cylinder of radius 2b and height 2a is _______.
(ii) Volume of a cylinder with radius p and height q is __________.
(iii) 6.55m² = ______cm²
(iv)The volume of a cylinder becomes __________ the original volume if its radius becomes doubles of the original radius and height becomes half of its original values
Ans: 
(i) S = 2πrH = 2π2b2a = 8πab
(ii) V=πr²H = πp²q
(iii) 6.55m² =6.55 x 10⁴ cm²
(iv) V₁= πr²H, V2=π(2r)²(1/2)H=2πr²H, So it becomes double

Q3: The parallel sides of a trapezium are 20 cm and 10 cm. Its nonparallel sides are both equal, each being 13 cm. Find the area of the trapezium. 
Sol: Let ABCD is the trapezium with AB and CD are the parallel sides.
Now
AB=10 cm, CD=20 cm, BC=13 cm
Now draw line BE || AD and draw a perpendicular from B on EC
Now ABED is a parallelogram, then BE=13 cm
In triangle BEC, BE =BC, So Isoceles triangle,So perpendicular will bisect the EC
Hence EF = FC
Now EC=  DC -DE = 20 -10 =10 cm
Therefore EF = FC = EC/2 = 5 cm
Now in Triangle BEF, it is right angle at F,So by pythagorous theorem
BE² = BF² + EF²
169 = BF² + 25
BF= 12cm
This is also the perpendicular distance between the parallel sides. So now coming back to Area of trapezium
A = 1/2[a + b] × h
Here a = 10 cm , b = 20 cm, h = 12 cm., A =?
Therefore
A = 1/2[10 + 20]×12
A = 180cm<sup>2

Q4: Mitesh wants to buy a trapezium shaped field. Its side along the river is parallel to and twice the side along the road. If the area of this field is 10500 m2 and the perpendicular distance between the two parallel sides is 100 m, find the length of the side along the river.
Sol: 
let x be the length on the road, then 2x is the length on the river side
Area of trapezium=Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the
A = 1/2[a + b] × h
Here a = 2x m , b = x, h = 100 m., A = 10500 m2
Therefore
10500 = 1/2[2x + x] × 100
x = 70 m
So parallel sides are 70 m and 140 m.</sup>

Q5: The area of a trapezium is 1586 cm² and the distance between its parallel sides is 26 cm. If one of the parallel sides is 84 cm, find the other.
Sol:
Area of trapezium=Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the
A = 1/2[a + b] × h
Here a = 84 cm , b = ?, h = 26 cm., A = 1586 cm²
Therefore
1586 = 1/2[84 + b] × 26
 h= 38cm

Q6: Find the area of a trapezium whose parallel sides are 38.7 cm and 22.3 cm, and the distance between them is 18 cm.
Sol:
Area of trapezium=Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the
A = 1/2[a + b] × h
Here a = 38.7 cm , b = 22.3 cm h = 18 cm
Therefore
A = 1/2[38.7 + 22.3] × 18
= 549cm²

Q7: Find the area of a trapezium whose parallel sides are 12 cm and 20 cm and the distance between them is 15 cm.
Sol:
Area of trapezium = Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the
A = 12[a + b] × h
Here a = 12 cm , b = 20 cm h =15 cm
Therefore
A = 12[12 + 20] × 15 
= 240cm²

Q8: The area of a trapezium is 1440 cm². If the lengths of its parallel sides are 54.6 cm and 35.4 cm, find the distance between them. 
Sol:
Area of trapezium = Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the
A = 1/2[a + b] × h
Here a = 54.6 cm , b = 35.4 cm, h = ?, A = 1440 cm²
Therefore
1440 = 1/2[38.7 + 22.3] × h
h = 32 cm 

Q9: The area of a trapezium is 384cm². Its parallel sides are in the ratio 2: 6 and the perpendicular distance between them is 12 cm. Find the length of each of the parallel sides. 
Sol:
Area of trapezium=Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the
A = 12[a + b] × h
Here a = 2x cm , b = 6x, h = 12 cm., A = 384 cm²
Therefore
384 = 12[2x + 6x] × 12
x = 8 cm
So parallel sides are 16 cm and 48 cm 

Q10: The area of a trapezium is 180 cm² and its height is 9 cm. If one of the parallel sides is longer than the other by 6 cm, find the two parallel sides.
Sol:
let x be one side, then x+6 is the length of another parallel side
Area of trapezium = Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the
A=12[a + b] × h
Here a = x m , b = x + 6, h = 9 cm., A= 180 cm²
Therefore
180 = 12[x + x + 6] × 9
= 17 cm
So parallel sides are 17 cm and 23 cm 

Q11: True & False
(i) Amount of region occupied by a solid is called its surface area
(ii)The areas of any two faces of a cube are equal.
(iii)The areas of two oppossite faces of a cuboid are equal.
(iv) 2.5 litres is equal to 0.0025 cubic meters
(v) Ratio of area of a circle to the area of a square whose side equals radius of circle is 1 : π.
Ans:
(i) False
(ii) True
(iii) True
(iv) True
(v) false

Q12: Match the column.

Ans: