# Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 2 Measurements Ex 2.2

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## Tamilnadu Samacheer Kalvi 7th Maths Solutions Term 2 Chapter 2 Measurements Ex 2.2

Question 1.
Find the area of the dining table whose diameter is 105 cm.
Solution:
Diameter of the dinig table (d) = 105 cm
∴ Radius r = $$\frac { d }{ 2 }$$ = $$\frac { 105 }{ 2 }$$ cm
Area of the circle = π r2 = $$\frac { 22 }{ 7 }$$ × $$\frac { 105 }{ 2 }$$ × $$\frac { 105 }{ 2 }$$ = 8662.5 sq.cm
Area of the dinning table = 8662.5 cm2

Question 2.
Calculate the area of the shotput ring whose diameter is 2.135 m.
Solution:
Radius of the shotput ring r = $$\frac { d }{ 2 }$$ = $$\frac { 2.135 }{ 2 }$$ m
Area of the circle = π r2
= $$\frac { 22 }{ 7 }$$ × $$\frac { 2.135 }{ 2 }$$ × $$\frac { 2.135 }{ 2 }$$
= $$\frac { 25.07 }{ 7 }$$ = 3.581 m2
∴ Area of the shotput ring = 3.581 m2

Question 3.
A sprinkler placed at the centre of a flower garden sprays water covering a circular area. If the area watered is 1386 cm2, find its radius and diameter.
Solution:
Area of the Circle = π r2 sq.units
Area of the circular portion watered = 1386 cm2
π r2 = 1386
$$\frac { 22 }{ 7 }$$ × r2 = 1386
r2 = 1386 × $$\frac { 7 }{ 22 }$$ = 63 × 7 = 9 × 7 × 7
r2 = 32 × 72
r = 3 × 7
Diameter (d) = 2 r = 2 × 21 cm
Diameter (d) = 42 cm

Question 4.
The circumference of a circular park is 352 m. Find the area of the park.
Solution:
Circumference of a Circle = 2 π r units
Given circumference of a circular park = 352 m
2 π r = 352
2 × $$\frac { 22 }{ 7 }$$ × r = 352
r = 352 × $$\frac { 7 }{ 22 }$$ × $$\frac { 1 }{ 2 }$$ = 56 m
Area of the park = π r2 = $$\frac { 22 }{ 7 }$$ × 56 × 56 sq.units
= 22 × 8 × 56 = 9856 m2
∴ Area of the Circular park = 9856 m2

Question 5.
In a grass land, a sheep is tethered by a rope of length 4.9 m. Find the maximum area that the sheep can graze.

Solution:
Length of the rope = 4.9 m
Area that the sheep can graze = Area of circle with radius 4.9m
Area of the circle = π r2 sq.units
= $$\frac { 22 }{ 7 }$$ × 4.9 × 4.9 = 22 × 0.7 × 4.9 = 75.46
∴ Area that the sheep can graze = 75.46 m2

Question 6.
Find the length of the rope by which a bull must be tethered in order that it may be able to graze an area of 2464 m2.
Solution:
If the bull is tethered by a rope then the area it can graze is a circular area of radius
= length of the rope
Area of the circle = 2464 m2
π r2 = 2464 m2
$$\frac { 22 }{ 7 }$$ × r2 = 2464
r2 = 2464 × $$\frac { 7 }{ 22 }$$ = 122 × 7 = 16 × 7 × 7
r2 = 42 × 72
r = 4 × 7 = 28 m
length of the rope r = 28 m

Question 7.
Lalitha wants to buy a round carpet of radius is 63 cm for her hall. Find the area that will be covered by the carpet.
Solution:
Radius of the round carpet = 63 cm
Area covered by the round carpet = πr2 sq units
A = $$\frac { 22 }{ 7 }$$ × 63 × 63 = 22 × 9 × 63 = 12474 cm2
Area covered by the round carpet = 12,474 cm2

Question 8.
Thenmozhi wants to level her circular flower garden whose diameter is 49 m at the rate of ₹150 per m2 Find the cost of levelling.
Solution:
Diamter of the circular garden d = 49 m
Radius r = $$\frac { d }{ 2 }$$ = $$\frac { 49 }{ 2 }$$ m
Area of the circular garden = πr2 sq units
= $$\frac { 22 }{ 7 }$$ × $$\frac { 49 }{ 2 }$$ × $$\frac { 49 }{ 2 }$$ m2 = 1,886.5 m2
Cost of levelling a m2 area = ₹ 150
∴ Cost of levelling 1886.5 m2 = ₹ 150 × 1886.5 = ₹ 2,82,975
Cost of levelling the flower garden = ₹ 2,82,975

Question 9.
The floor of the circular swimming pool whose radius is 7 m has to be cemented at the rate of ₹ 18 per m2. Find the total cost of cementing the floor.
Solution:
Radius of the circular swimming pool r = 7 m
Area of the circular swimming pool A = πr2 sq. units
= $$\frac { 22 }{ 7 }$$ × 7 × 7 m2 = 154 m2
Cost of cementing a m2 floor = ₹ 18.
Cost of cementing 154 m2 floor = ₹ 18 × 154 = ₹ 2,772

Objective Type Questions

Question 10.
The formula used to find the area of the circle is
(i) 47πr2
(ii) πr2
(iii) 2πr2
(iv) πr2 + 2r
(ii) πr2

Question 11.
The ratio of the area of a circle to the area of its semicircle is
(i) 2 : 1
(ii) 1 : 2
(iii) 4 : 1
(iv) 1 : 4