Mathematics Semester i Solutions Solutions for Class 7 Math Chapter 7 Geometry are provided here with simple step-by-step explanations. These solutions for Geometry are extremely popular among class 7 students for Math Geometry Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Semester i Solutions Book of class 7 Math Chapter 7 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s Mathematics Semester i Solutions Solutions. All Mathematics Semester i Solutions Solutions for class 7 Math are prepared by experts and are 100% accurate.
Page No 91:
Question O1:
What is a circle?
Answer:
A circle is a path traced by a moving point, which is equidistant from a fixed point. This fixed point is called a centre.
Page No 91:
Question O2:
What is the diameter of a circle whose radius is 7 cm?
Answer:
14 cm
Page No 91:
Question O3:
What is the radius of a circle whose diameter is 4.8 cm?
Answer:
2.4 cm
Page No 92:
Question W1:
Fill in the blanks with suitable words:
1. Diameter of a circle is _______ its radius.
2. Radius of a circle is ______ its diameter.
3. The diameters of a circle intersect at the ______.
4. The chord passing through the centre of a circle is _________.
5. The biggest chord of a circle is ______.
6. The lengths of the radii of a circle are _______.
Answer:
1. Diameter of a circle is twice its radius.
2. Radius of a circle is half its diameter.
3. The diameters of a circle intersect at the centre.
4. The chord passing through the centre of a circle is diameter.
5. The biggest chord of a circle is diameter.
6. The lengths of the radii of a circle are equal.
Page No 92:
Question W2:
The diameters of circles are given below. Find their radii.
(1) 8 cm
(2) 6 cm
(3) 8.6 cm
(4) 5.4 cm
Answer:
(1) r =
=
= 4 cm
(2) r =
=
= 3 cm
(3) r =
=
= 4.3 cm
(4) r =
=
= 2.7 cm
Page No 92:
Question W3:
Find the diameters of the circles whose radii are given below.
(1) 5 cm
(2) 7 cm
(3) 2.4 cm
(4) 3.7 cm
Answer:
Diameter (d) = 2r, r being the radius
(1) d = 2r = (2 × 5) cm = 10 cm
(2) d = 2r = (2 × 7) cm = 14 cm
(3) d = 2r = (2 × 2.4) cm = 4.8 cm
(4) d = 2r = (2 × 3.7) cm = 7.4 cm
Page No 92:
Question W4:
Using ruler and compass draw circles with the radii given below.
Mark their centres and draw the radii.
(1) 4 cm
(2) 2.5 cm
Answer:
(1)
(2)
Page No 92:
Question W5:
Draw circles with the following radii. Draw and name the diameters. Also measure their lengths.
(1) 3 cm
(2) 3.8 cm
Answer:
(1)
Length of diameter AB = 6 cm
(2)
Length of diameter PQ = 7.6 cm
Page No 92:
Question W6:
Draw circles of the given radii and draw chords of the given lengths.
Sl. No. |
Radius (cm) |
Length of chord (cm) |
1. 2. |
2.5 4.0 |
3.0 3.5 |
Answer:
(1) Construction:
Taking O as centre and radius OR = 2.5 cm, draw a circle.
With the help of a ruler, draw a chord of 3cm length as shown below.
(2) Construction:
Taking O as centre and radius OR = 4.0cm, draw a circle.
With the help of a ruler, draw a chord of 3.5 cm length as shown below.
Page No 92:
Question W7:
Draw a circle with radius 4.3 cm. Draw a segment with the length of its chord as 6.5 cm and name the segment.
Answer:
Taking O as centre and radius OR = 4.3 cm, draw a circle.
With the help of a ruler, draw a chord of 6.5cm length as shown below.
And the area between the chord AB and arc AB is the required segment APB.
Page No 95:
Question O1:
What is the approximate value of π?
Answer:
The approximate value of π is .
Page No 95:
Question W1:
Find the circumference of circles whose radii are
(1) 21 cm
(2) 56 cm
(3) 4.2 cm
(4) 10.5 cm
Answer:
(1) C = 2πr
= 2 × × 21
= 2 × 22 × 3
= 132 cm
(2) C = 2πr
= 2 × × 56
= 2 × 22 × 8
= 352 cm
(3) C = 2πr
= 2 × × 4.2
= 2 × 22 × 0.6
= 26.4 cm
(4) C = 2πr
= 2 × × 10.5
= 2 × 22 × 1.5
= 66 cm
Page No 95:
Question O2:
What is the formula to find the circumference of a circle?
Answer:
The circumference of a circle is the product of π and its diameter. Thus, the formula to find the circumference of a circle is .
Page No 95:
Question W2:
Find the circumference of circles whose diameters are
(1) 7 cm
(2) 14 cm
(3) 3.5 cm
(4) 5.6 cm
Answer:
(1) C = πd
= × 7
= 22 cm
(2) C = πd
= × 14
= 44 cm
(3) C = πd
= × 3.5
= 11 cm
(4) C = πd
= × 5.8
= 17.6 cm
Page No 95:
Question W3:
Find the diameter of circles whose circumference is
(1) 22 cm
(2) 44 cm
(3) 8.8 cm
(4) 13.2 cm
Answer:
We know that, C = πd. So, d =
(1)
(2)
(3)
(4)
Page No 95:
Question O3:
If C = πd, then what is the value of d?
Answer:
If , then .
Page No 97:
Question W1:
The diameter of a wheel is 15.4 cm. Calculate the distance travelled when it completes 150 revolutions.
Answer:
C = πd = ×15.4 cm = 48.4 cm
Distance travelled when the wheel completes one revolution = 48.4 cm
∴ Distance travelled when the wheel completes 150 revolution = 48.4 × 150 cm = 7260 cm
Page No 97:
Question W2:
The diameter of a bicycle wheel is 56 cm. Find the distance travelled when it completes 250 revolutions.
Answer:
C = πd = ×56 cm = 176 cm
Distance travelled when the wheel completes one revolution = 176 cm
∴ Distance travelled when the wheel completes 250 revolution = 176 × 250 cm = 44000 cm
Page No 98:
Question W3:
The circumference of a bicycle wheel is 132 cm. How many revolutions does it complete when it move a distance of 264 m?
Answer:
C = 132 cm
Distance Travelled = 264 m = 26400 cm
∴Number of revolutions = = = 200
Page No 98:
Question W4:
The radius of the wheel of a car is 98 cm. Find the number of revolutions it completes, when it travels a distance of 3.850 m.
Answer:
C = 2πr
= 2 × × 98
= 2 × 22 × 14
= 616 cm
Distance Travelled = 3850 m = 385000 cm
∴ Number of revolutions = = = 625
Page No 98:
Question W5:
The distance covered by a wheel when it completes 20 revolutions is 110 m. Find the diameter of the wheel.
Answer:
Number of revolutions =
20 =
C =
C = 5.5 m = 550 cm
C = πd
550 = × d
d =
d = 175 cm = 1.75 m
Page No 98:
Question W6:
A wheel covers a distance of 82.5 m is 15 revolutions. Find its diameter.
Answer:
Number of revolutions =
15 =
C =
C = 5.5 m = 550 cm
C = πd
550 = × d
d =
d = 175 cm = 1.75 m
Page No 100:
Question O1:
What is the formula to find the area of a circle?
Answer:
The formula to find the area of a circle is .
Page No 100:
Question W1:
Find the areas of circles whose radii are
(1) 14 cm
(2) 21 cm
(3) 10.5 cm
(4) 3.5 cm
Answer:
(1) Area, A = πr^{2 }= π × r × r = × 14 × 14 = 616 cm^{2}
(2) Area, A = πr^{2 }= π × r × r =× 21 × 21 = 1386 cm^{2}
(3) Area, A = πr^{2 }= π × r × r = × 10.5 × 10.5 = 346.5 cm^{2}
(4) Area, A = πr^{2 }= π × r × r =× 3.5 × 3.5 = 38.5 cm^{2}
Page No 100:
Question O2:
Which of the following is area of a circle?
(a) 154 m
(b) 154 sq. m
(c) 154 cm
Answer:
(a) The unit of the quantity 154 m is m (meter). Thus, it is not the area of a circle.
(b) The unit of the quantity 154 sq. m is sq. m (square meter). Thus, it is the area of a circle.
(c) The unit of the quantity 154 cm is cm (centimeter). Thus, it is not the area of a circle.
Page No 101:
Question W2:
Find the areas of circles whose diameters are
(1) 28 cm
(2) 42 cm
(3) 7 cm
(4) 70 cm
Answer:
(1) r =
=
= 14 cm
A = πr^{2}
A = π × r × r
= × 14 × 14
= 616 cm^{2}
(2) r =
=
= 21 cm
A = πr^{2}
A = π × r × r
= × 21 × 21
= 1386 cm^{2}
(3) r =
=
= 3.5 cm
A = πr^{2}
A = π × r × r
= × 3.5 × 3.5
= 38.5 cm^{2}
(4) r =
=
= 35 cm
A = πr^{2}
A = π × r × r
= × 35 × 35
= 3850 cm^{2}
Page No 101:
Question W3:
Find the radii of circles whose areas are
(1) 1.386 cm^{2}
(2) 15,400 sq. cm
Answer:
(1) A = πr^{2}
i.e. 1386 = × r^{2}
i.e. × r^{2 }= 1386
r^{2 }= 1386 ×
r^{2 }= 441 = 21^{2}
∴ r = 21 cm
(2) A = πr^{2}
i.e. 15400 = × r^{2}
i.e. × r^{2 } = 15400
r^{2 }= 15400 ×
r^{2 }= 4900 = 70^{2}
∴ r = 70 cm
Page No 101:
Question W4:
Find the area of circles whose circumference are
(1) 88 cm
(2) 7π cm
Answer:
(1) C = 2πr
88 = 2 × × r
r =
r = 14 cm
A = πr^{2}
A = π × r × r
= × 14 × 14
= 616 cm^{2}
(2) C = 2πr
7π = 2 × π× r
Cancelling π on both the sides of the equation:
r =
r = 3.5 cm
A = πr^{2}
A = π × r × r
= × 3.5 × 3.5
= 38.5 cm^{2}
Page No 102:
Question W1:
Find the area of the shaded potion
Answer:
Diameter of the circle, d = 14 cm
Radius of the circle, r =
=
= 7 cm
Area of the circular region, A = πr^{2}
= π × r × r
= × 7 × 7
= 154 cm^{2}
Area of the rectangular region = l × b
= 14 × 14
= 196 cm^{2}
Area of the shaded portion = Area of the rectangular region − Area of the circular region
= 196 − 154
= 42 cm^{2}
Page No 102:
Question W2:
Find the areas of sectors A, B and C
Answer:
We know:
Area of a circle =
= r r
= 14 14
= 44 14
= 616
Area of sector A = Area of the circle
= 616
= 154
Area of sector B = Area of the circle
= 616
= 308
Area of sector C = Area of the circle
= 616
= 154
Page No 102:
Question W3:
The inner and outer radii of a circular ring are 14 cm and 21 cm respectively. Find the area of the shaded portion.
Answer:
We know:
Area of the circle =
Area of the inner circle =
= r r
= 14 14
= 44 14
= 616
Area of the outer circle =
= r r
= 21 21
= 66 21
= 1386
Area of the shaded portion = Area of the outer circle − Area of the inner circle
= 1386 − 616
= 770
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