Mensuration Class-8 ML Aggarwal ICSE Maths Solutions

Mensuration Class-8 ML Aggarwal ICSE Mathematics Solutions Chapter-18. We provide step by step Solutions of Exercise / lesson-18 Mensuration Class-8th ML Aggarwal ICSE Mathematics.

Our Solutions contain all type Questions with Exe-18.1 , Exe-18.2 , Exe-18.3, Exe-18.4 , Objective Type Questions (including Mental Maths Multiple Choice Questions, Value Based Questions , HOTS ), and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.


— : Select Topics : —

Exe-18.1,

 Exe-18.2 ,

 Exe-18.3,

 Exe-18.4

Objective Type Questions, 

Mental Maths,

Multiple Choice Questions ,(MCQ)

Value Based Questions 

HOTS

Check Your Progress

Ex 18.1, Mensuration Class-8 ML Aggarwal ICSE Mathematics Solutions

Question 1.

The length and breadth of a rectangular field are in the ratio 9 : 5. If the area of the field is 14580 square metres, find the cost of surrounding the field with a fence at the rate of ₹3·25 per metre.

Answer

Let the length = 9x and the breadth = 5x
Area = l × b ⇒ 14580 = 9x × 5x
⇒ 45x2 = 14580
∴ x2 = \frac{14580}{45} = 324 ⇒ x = \sqrt{324}
⇒ x = \sqrt{18 \times 18}
or x = 18
Length = 9 × 18 = 162 m
Breadth = 5 × 18 = 90 m
Perimeter = 2(l + b)
= 2 (162 + 90) = 2(252)
= 504 m.
∴ Cost for 504 m fencing the surrounding
at the rate of ₹3·25 per metre = ₹(504 × 3·25) = ₹1638

Question 2.
A rectangle is 16 m by 9 m. Find a side of the square whose area equals the area of the rectangle. By how much does the perimeter of the rectangle exceed the perimeter of the square?

Answer

Area of rectangle = (16 × 9) m2 = 144 m2
Area of square = Area of rectangle (given)
∴ (side)2 = 144
Side = \sqrt{144}=\sqrt{12 \times 12} = 12 m
Perimeter of square = 4 × 12 = 48 m
Perimeter of rectangle = 2(l + b) = 2 (16 + 9) = 50 m
Difference in their perimeters = 50 – 48 = 2 m

Question 3.
Two adjacent sides of a parallelogram are 24 cm and 18 cm. If the distance between longer sides is 12 cm, find the distance between shorter sides.

Answer

Taking 24 cm as a base of parallelogram, its height is 12 cm.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 1
∴ Area of parallelogram = b × h = 24 × 12 = 288 cm2
Let d cm be the distance between the shortest sides.
∴ Area of parallelogram = (18 × d) cm2
⇒ 18 × d = 288
⇒ d = \frac{288}{18} = 16 cm

Question 4.
Rajesh has a square plot with the measurement as shown in the given figure. He wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of ₹50 per m2.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 2

Answer

Side of square plot = 24 m
Length of house (l) = 18 m
and breadth (b) = 12m
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 3
Now area of square plot = (24)2 m2 = 24 × 24 = 576 m2
and area of hosue = 18 × 12 = 216 m2
Remaining area of the garden = 576 – 216 = 360 m2
Cost of developing the garden = ₹50 per m2
Total cost = ₹50 × 360 = ₹18000

Question 5.
A flooring tile has a shape of a parallelogram whose base is 18 cm and the corresponding height is 6 cm. How many such tiles are required to cover a floor of area 540 m2? (If required you can split the tiles in whatever way you want to fill up the comers).

Answer

Base of the parallelogram-shaped flooring tile = 18 cm
and height = 6 cm
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 4
∴ Area of one tile = Base × Height = 18 × 6 = 108 cm2
Area of floor = 540 m2
∴ Number of tiles = \frac{\text { Total area }}{\text { Area of one tile }}
\frac{540 \times 100 \times 100}{108} = 50000

Question 6.
An ant is moving around a few food pieces of different shapes scattered on the floor. For which food piece would the ant have to take a longer round?
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 6

Answer

(a) Diameter of semicircle = 2.8 cm
∴ Perimeter = πr + 2r
\frac{22}{7} × 2.8 + 2 × 2.8
= 8.8 + 5.6 cm = 14.4 cm
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 7

(b) Total perimeters
= 1.5 + 1.5 + 2.8 + Semi circular
= 5.8 + 8.8 = 14.6 cm
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 8
(c) Total perimeter = 2 + 2 + Semi circumference
= 4 + 8.8 = 12.8 cm
It is clear that distance of (b) i.e. 14.6 is longer.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 9

Question 7.
In the adjoining figure, the area enclosed between the concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 10

Answer

Radius of outer circle (R) = 21 cm.
radius of inner circle (r) = r cm.
Area of shaded portion = 770 cm2
⇒ π (R2 – r2) = 770
⇒ \frac{22}{7} (212 – r2) = 770
⇒ 441 – r2 = 770 × \frac{7}{22} = 35 × 7 = 245
⇒ r2 = 441 – 245
⇒ r2 = 196
⇒ r2 = 196
⇒ r = \sqrt{196}=\sqrt{14 \times 14}
⇒ r = 14 cm

Question 8.
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.

Answer

Area of the square = 121 cm2
∴ Side = \sqrt{121}=\sqrt{11 \times 11} = 11 cm
Perimeter = 4 a = 4 × 11= 44 cm
Now, circumference of the circle = 44 cm
∴ Radius = \frac{44 \times 7}{2 \times 22} = 7cm
and area of the circle = πr2 = \frac{22}{7}(7)2
\frac{22}{7} × 7 × 7 = 154 cm2

Question 9.
From the given figure, find
(i) the area of ∆ ABC
(ii) length of BC
(iii) the length of altitude from A to BC
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 11

Answer

(i) Base = 3 cm, height = 4 cm.
Area = \frac{1}{2} × base × height
\frac{1}{2} × 3 × 4 = 6 cm2
(ii) By pythagoras theorem,
BC2 = AB2 + AC2
∴ BC2 = (3)2 + (4)2
= 9 + 16 = 25
⇒ BC = \sqrt{25} cm = 5 cm
(iii) Now, Base = BC = 5 cm., h = AD = ?
Area = \frac{1}{2} × b × h
⇒ 6 = \frac{1}{2} × 5 × h
[∵ Area = 6 cm2 as in part (i)] ⇒ h = \frac{12}{5} = 2·4 cm.

Question 10.
A rectangular garden 80 m by 40 m is divided into four equal parts by two cross-paths 2.5 m wide. Find
(i) the area of the cross-paths.
(ii) the area of the unshaded portion.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 12

Answer

Length of rectangular garden = 80 m
and breadth = 40 m
Width of crossing path 2.5 m
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.1 13
Area of length wise path
= 80 × 2.5 = 200 m2
Area of breadth wise path
= 40 × 2.5 = 100 m2
(i) Total area of both paths
= 200 + 100 – 2.5 × 2.5 m2
= 300 – 6.25 = 293.75 m2
(ii) Area of unshaded portion
= Area of garden – Area of paths
= 80 × 40 – 293.75 m2
= 3200 – 293.75 m2
= 2906.25 m2

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