## Maharashtra State Board Class 7 Maths Solutions Chapter 11 Circle Practice Set 42

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 Activities**

Question 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