WBBSE Class 9 Maths Mensuration Chapter 2 Circumference Of Circle Multiple Choice Questions

WBBSE Class 9 Maths Mensuration Chapter 2 Circumference Of Circle Multiple Choice Questions

Example 1. The ratio of the velocity of the hour’s hand and minute’s hand at a clock is

1. 1: 12
2. 12: 1
3. 1: 2h
4. 2h: 1

Solution: Let the length of the radius of the clock = r unit

∴ In 1 hour hour’s hand covers = \(\frac{2 \pi r}{12}\) unit

In h hour minute’s hand covers 2πr unit

∴ Ratio = \(\frac{2 \pi r}{12}\): 2πr = \(\frac{1}{2}\): 1 = 1: 12

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∴ The correct answer is 1. 1: 12

Example 2. Some take \(\frac{\pi x}{100}\) minute to go one completer round of a circular path. Soma will take time for going round the park diametrically.

1. \(\frac{x}{200}\)minutes
2. \(\frac{x}{100}\)minutes
3. \(\frac{\pi}{100}\)minutes
4. \(\frac{\pi}{200}\)minutes

Solution: Soma covers 2πr unit in \(\frac{\pi x}{100}\)

Some covers 2r unit in \(\frac{\pi}{100}\) minute

∴ The correct answer is 3. \(\frac{\pi}{100}\)minutes

Example 3. A circle is inscribed by a square. The length of side of square is 10 cm. The length of diameter of circle is

1. 10 cm
2. 5 cm
3. 20 cm
4. 10√2 cm

Solution: Length of the side of the square

= Diameter of the circle = 10 cm

∴ The correct answer is 1. 10 cm

∴ The length of diameter of circle is 10 cm

Example 4. A circle circumscribed a square. The length of side of square is 5 cm. The length of diameter of circle is

1. 5√2 cm
2. 10√2 cm
3. 5 cm
4. 10 cm

Solution: Length of the diameter = Length of the diagonal of the square = 5√2 cm.

∴ The correct answer is 1. 5√2 cm

∴ The length of diameter of circle is 5√2 cm

Example 5. A circular ring is 5 cm wide. The difference of outer and inner radius is

1. 5 cm
2. 2.5 cm
3. 10 cm
4. None of these

Solution: difference of outer and inner radius = width of the rise = 5 cm

∴ The correct answer is 1. 5 cm

∴ The difference of outer and inner radius is 5 cm

Example 6. The radius of a semi-circular plate is 3.5 cm. It is perimeter is one of the following

1. 18 cm
2. 22 cm
3. 11 cm
4. None of these

Solution: The length of semi-circumference = πr = \(\frac{22}{7}\) x 3.5 cm = 11 cm

Length of the diameter = 2 x 3.5 cm = 7 cm

Total length of its perimeter = (11 + 7) cm = 18 cm

∴ The correct answer is 1. 18 cm

∴ perimeter of a semi-circular plate is 18 cm

Example 7. There is a path of uniform width along the inner boundary of a circular park. The outer circumference of the path is 729 m and inner circumference of the paths is 770 m. Width of the path is

1. 3.5 m
2. 7 m
3. 7.5 m
4. None of these

Solution: 2πR – 2πr = 792 -770

or, R – r = \(\frac{22 \times 7}{2 \times 22}=\) = 3.5

∴ The correct answer is 1. 3.5 m

∴ Width of a circular park path is 3.5 m 

Example 8. Ratio of circum radius and inradius of a square is

1. 1: √2
2. √2: 1
3. 1: 2
4. 2: 1

Solution: Let length of the square be a unit.

Circum radius = \(\frac{1}{2}\) diagonal of a square = \(\frac{\sqrt{2 a}}{2}\) unit

in radius = \(\frac{a}{2}\) unit

∴ Ratio = \(\frac{\sqrt{2 a}}{2}\): \(\frac{a}{2}\) = √2: 1

∴ The correct answer is 2. √2: 1

∴ Ratio of circum radius and inradius of a square is √2: 1

Example 9. Length of a minute hand in 7 cm. It covers in 15 minute

1. 11 cm
2. 22 cm
3. 1.1 cm
4. 2.2 cm

Solution: In 15 minutes hand covers

= \(\frac{\frac{2 \times 22}{7} \times 7}{60} \times 15\) cm = 11 cm

∴ The correct answer is 1. 11 cm

Example 10. Perimeter of a semicircle is 36 cm. Length of its diameter is

1. 14 cm
2. 22 cm
3. 21 cm
4. None of these

Solution: πr + 2r = 36

⇒ r (π + 2) = 36

r x \(\frac{36}{7}\) = 36. ⇒ r = 7

Length of diameter = 7 x 2 cm = 14 cm

∴ The correct answer is 1. 14 cm

∴ Length of its diameter of semicircle 14 cm.