Maharashtra Board Class 7 Math Solution Chapter 11 – Circle
Balbharati Maharashtra Board Class 7 Math Solution Chapter 11: Circle. Marathi or English Medium Students of Class 7 get here Circle full Exercise Solution.
Std |
Maharashtra Class 7 |
Subject |
Math Solution |
Chapter |
Circle |
Practice Set 42
1.) Complete the table below.
ANS:
i)
Given that,
Radius of circle = 7 cm.
We know,
Diameter of circle = 2 x Radius.
Diameter of circle = 2 x 7
Diameter of circle = 14 cm.
Circumference of circle = π x Diameter.
Circumference of circle =π x 14
WE know,
Value of π = 22/7
Circumference of circle =22/7 x 14
Circumference of circle = 44 cm.
ii) Given that,
Diameter of circle = 28 cm.
We know,
Diameter of circle = 2 x Radius.
Radius of circle = Diameter / 2
Radius of circle = 28 / 2
Radius of circle = 14 cm.
Now,
Circumference of circle = π x Diameter.
Circumference of circle = π x 28
WE know,
Value of π = 22/7
Circumference of circle = 22/7 x 28
Circumference of circle = 88 cm.
iii) Given that,
Circumference of circle = 616 cm
Circumference of circle = π x Diameter.
WE know,
Value of π = 22/7
Diameter of circle =Circumference of circle x 7 / 22
Diameter of circle = 616 x 7 / 22
Diameter of circle = 28 x 7
Diameter of circle = 196 cm
We know,
Diameter of circle = 2 x Radius.
Radius of circle = Diameter / 2
Radius of circle = 196 / 2
Radius of circle = 98 cm.
iv) Given that,
Circumference of circle = 72.6 cm
Circumference of circle = π x Diameter.
WE know,
Value of π = 22/7
Diameter of circle = Circumference of circle x 7 / 22
Diameter of circle = 72.6 x 7 / 22
Diameter of circle = 3.3 x 7
Diameter of circle = 23 cm
We know,
Diameter of circle = 2 x Radius.
Radius of circle = Diameter / 2
Radius of circle = 23 / 2
Radius of circle = 11.5 cm.
2.) If the circumference of a circle is 176 cm, find its radius.
ANS:
Given that,
Circumference of a circle is 176 cm
Circumference of circle = π x Diameter.
WE know,
Value of π = 22/7
Diameter of circle = Circumference of circle x 7 / 22
Diameter of circle = 176 x 7 / 22
Diameter of circle = 8 x 7
Diameter of circle = 56 cm
We know,
Diameter of circle = 2 x Radius.
Radius of circle = Diameter / 2
Radius of circle = 56 / 2
Radius of circle = 28 cm.
3.) The radius of a circular garden is 56 m. What would it cost to put a 4-round fence around this garden at a rate of 40 rupees per metre?
ANS:
Given that,
The radius of a circular garden is 56 m.
We have to find its circumference to fence around this garden at a rate of 40 rupees per metre.
We know,
Diameter of circle = 2 x Radius.
Diameter of circle = 2 x 56
Diameter of circle = 112 m.
Circumference of circle = π x Diameter.
Circumference of circle = π x 112
WE know,
Value of π = 22/7
Circumference of circle = 22/7 x 112
Circumference of circle = 22 x 16
Circumference of circle = 352 m.
We have to fence 4 round of garden.
352 m x 4 = 1408 m
We have to find cost of 4-round fence around garden at a rate of 40 rupees per metre.
1408 m x 40 = Rs.56, 320
Cost of 4-round fence around garden at a rate of 40 rupees per metre is Rs.56, 320
4.) The wheel of a bullock cart has a diameter of 1.4m. How many rotations will the wheel complete as the cart travels 1.1 km?
ANS:
Given that,
The wheel of a bullock cart has a diameter of 1.4 m.
We have to find total number of rotation of wheels to travel distance of 1.1 km.
Diameter of wheel = 1.4 m
We have to find first the circumference of a wheel.
Circumference of a wheel = π x Diameter.
Circumference of circle = π x 1.4 m
WE know,
Value of π = 22/7
Circumference of circle = 22/7 x 1.4
Circumference of circle = 22 x 0.2
Circumference of circle = 4.4 m.
Number of wheel Rotations= Total Distance / Circumference of wheel
Number of wheel Rotations = 1100 m / 4.4 m
Number of wheel Rotations = 250
250 rotations of the wheel complete as the cart travels 1.1 km.
Practice Set 43
1.) Choose the correct option.
If arc AXB and arc AYB are corresponding arcs and m(arc AXB) = 120° then m(arc AYB) = ____
ANS:
We know,
Measure of circle = 360^{0}
Given that,
Measure of minor arc m(arc AXB) = 120°
We have to find measure of major arc m(arc AYB).
Measure of major arc m(arc AYB) = 360^{0} – Measure of minor arc m(arc AXB)
Measure of major arc m(arc AYB) =360^{0} -120°
Measure of major arc m(arc AYB) = 240°
2.) Some arcs are shown in the circle with centre ‘O’. Write the names of the minor arcs, major arcs and semi-circular arcs from among them.
ANS:
Given that,
Circle having centre o.
We have to find names of the minor arcs, major arcs and semi-circular arcs.
Minor arcs =
The smaller part of circle is called minor arc when a chord divides the circle.
Arc PXQ
Arc PR
Arc RY
Arc XP
Arc XQ
Arc QY
Major arcs =
The Larger part of circle is called major arc when a chord divides the circle.
Arc PYQ
Arc PQR
Arc RQY
Arc XQP
Arc QRX
Semi-circular arcs =
When a chord or diameter of circle divides the circle in two equal parts then arc formed is semi-circular arc.
Arc QPR
Arc QYR
3.) In a circle with centre O, the measure of a minor arc is 110°. What is the measure of the major arc PYQ?
ANS:
Given that,
Measure of a minor arc PXQ is 110°
We have to find measure of major arc PYQ.
We know,
Measure of circle = 360^{0}
Measure of minor arc m (arc PXQ) = 110°
We have to find measure of major arc m (arc PYB).
Measure of major arc m (arc PYQ) = 360^{0} – Measure of minor arc m (arc PXQ)
Measure of major arc m (arc PYQ) = 360^{0} – 110°
Measure of major arc m (arc PYQ) = 250°