Balbharti
Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 42 Answers Solutions Chapter 11 Circle.
Question 1.
Complete the table below:
Sr. No |
Radius (r) |
Diameter (d) |
Circumference (c) |
i. |
7 cm |
|
|
ii. |
|
28 cm |
|
iii. |
|
|
616 cm |
iv. |
|
|
72.6 cm |
Solution:
i. Radius (r) = 7 cm
Diameter (d) = 2r
= 2 x 7 = 14 cm
Circumference (c) = πd
= \(\frac { 22 }{ 7 }\) x 14
= 44 cm
ii. Diameter (d) = 28 cm
Radius (r) = \(\frac{d}{2}=\frac{28}{2}\) = 14 cm
Circumference (c) = πd
= \(\frac { 22 }{ 7 }\) x 28
= 88 cm
iii. Circumference (c) = 616 cm
∴ πd = 616
∴ \(\frac { 22 }{ 7 }\) x d = 616
∴ d = 616 x \(\frac { 7 }{ 22 }\)
∴ d = 196 cm
∴ Diameter (d) = 196 cm
Radius (r) = \(\frac{\mathrm{d}}{2}=\frac{196}{2}\) = 98 cm
iv. Circumference (c) = 72.6 cm
∴ πd = 72.6
\(\frac { 22 }{ 7 }\) x d = 72.6
∴ \(d=72.6 \times \frac{7}{22}=\frac{726}{10} \times \frac{7}{22}=\frac{33 \times 7}{10}\)
∴ d = 23.1 cm
∴ Diameter (d) = 23.1 cm
Radius (r) = \(\frac{\mathrm{d}}{2}=\frac{23.1}{2}\)
= 11.55 cm
Sr. No |
Radius (r) |
Diameter (d) |
Circumference (c) |
i. |
7 cm |
14 cm |
44 cm |
ii. |
14 cm |
28 cm |
88 cm |
iii. |
98 cm |
196 cm |
616 cm |
iv. |
11.55 cm |
23.1 cm |
72.6 cm |
Question 2.
If the circumference of a circle is 176 cm, find its radius.
Solution:
Circumference (c) = 176 cm
∴ 2πr = 176
∴ 2 x \(\frac { 22 }{ 7 }\) x r = 176
∴ \(\frac { 44 }{ 7 }\) x r = 176
∴ r = 176 x \(\frac { 7 }{ 44 }\) = 28 cm
∴ The radius of the circle is 28 cm.
Question 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?
Solution:
Radius of the circular garden (r) = 56 m
∴ Circumference of the circular garden (c) = 2πr
= 2 x \(\frac { 22 }{ 7 }\) x 56
= 352 m
∴ Length of the wire required to put 1-round fence = Circumference
∴ Length of wire required to put a 4-round fence = 4 x Circumference
= 4 x 352
= 1408 m
∴ Cost of wire per meter = Rs 40
∴ Total cost = length of wire required x cost of the wire
= 1408 x 40
= Rs 56320
∴ The cost to put a 4-round fence around the garden is Rs 56320.
Question 4.
The wheel of a bullock cart has a diameter of 1.4 m. How many rotations will the wheel complete as the cart travels 1.1 km?
Solution:
Diameter of the wheel of the bullock cart (d) = 1.4 m
Circumference of the wheel of the bullock cart (c) = πd
\(=\frac{22}{7} \times 1.4=\frac{22}{7} \times \frac{14}{10}=\frac{44}{10}=4.4 \mathrm{m}\)
Distance covered in 1 rotation = Circumference of the wheel
= 4.4 m

∴ The wheel of the bullock cart will complete 250 rotations as the cart travels 1.1 km.
Maharashtra Board Class 7 Maths Chapter 11 Circle Practice Set 42 Intext Questions and ActivitiesQuestion 1.
Identify the radii, chords and diameters in the circle alongside and write their names in the table below: (Textbook pg. no. 75)
i. Radii |
|
ii. Chords |
|
iii. Diameters |
|

Solution:
i. OA, OB, OC, OF
ii. EC, AD, AB, FC
iii. AB, FC