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

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

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:

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
22/7 × r² = 1386
r² = 1386 × 7/22 = 63 × 7 = 9 × 7 × 7
r² = 3² × 7²
r = 3 × 7
Radius (r) = 21 cm
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 × 22/7 × r = 352
r = 352 × 7/22 × 1/2 = 56 m
Area of the park = π r² = 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
= 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
22/7 × r² = 2464
r² = 2464 × 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 = 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 = d/2 = 49/2 m
Area of the circular garden = πr² sq units
= 22/7 × 49/2 × 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
= 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
Answer:
(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
Answer:
(i) 2 : 1

Question 12.
Area of circle of radius ‘n’ units is
(i) 2πr^p sq.units
(ii) πm² sq.units
(iii) πr² sq.units
(iv) πn² sq.units
Answer:
(iv) πn² sq.units