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Correct OPTION is (d) \(\FRAC {\pi r^2}{2}\)

Easy explanation: A semicircle is half of a full circle. HENCE, the area of a semicircle is ALSO half of a circle. Half of πr^2 is \(\frac {\pi r^2}{2}\). Therefore, the area of a semicircle is \(\frac {\pi r^2}{2}\).

The correct OPTION is (C) Minor

Explanation: A SECTOR is a PART of a circle that is enclosed by two radii and an arc. The sector having a LARGER area is called a major sector and the sector having a smaller area is called a minor sector.

Right choice is (a) \(\frac {x^{\circ }}{360^{\circ }}\) × πr^2

The explanation is: The area of the sector is \(\frac {x^{\circ }}{360^{\circ }}\) × πr^2

Where x° is the DEGREE MEASURE of the angle at the center and r is the radius of the CIRCLE.

The correct answer is (c) 2.33 CM

To elaborate: CIRCUMFERENCE – Diameter = 10 cm(∵ Diameter = 2 × RADIUS)

2πr – 2r = 10 cm

2r(π – 1) = 10 cm

2r(\(\FRAC {22}{7}\) – 1) = 10 cm

2r(\(\frac {15}{7}\)) = 10 cm

r = 10 × \(\frac {7}{15} \times \frac {1}{2}\)

r = 2.33 cm

Correct choice is (a) 1.90 m

To elaborate: The CIRCUMFERENCE of a circle (C) = 2πr.

12 = 2 × \(\frac {22}{7}\) × R

r = \(\frac {12}{2} \TIMES \frac {7}{22}\)

r = 1.90 m

The CORRECT OPTION is (d) 760.57 cm

The best I can explain: The circumference of the circle (C) = 2πr

C = 2 × \(\FRAC {22}{7}\) × 121

A = 760.57 cm

Right OPTION is (c) 0.79 m

The best I can explain: One ROTATION of the wheel = circumference of the wheel

100 rotations = 500 m

1 rotation = 5 m

So, circumference = 5 m

2πr = 5 m

r = 5 × \(\frac {7}{22} \times \frac {1}{2}\)

r = 0.79m

Correct CHOICE is (b) C = 2πr

To explain I would say: The circumference of a circle (C) = 2πr.

Where C is the circumference of the circle and r is the radius of the given circle.

The value of π is TAKEN as \(\frac {22}{7}\).

Right option is (B) 6.54 m

The EXPLANATION: The area of the semicircle = πr^2/2

= (\(\FRAC {22}{7}\) × 6^2)/2

= 56.54 m

The correct answer is (c) 44 m

For explanation I would say: The circumference of a CIRCLE (C) = 2πr.

C = 2 × \(\frac {22}{7}\) × 7

C = 44 m

The CORRECT CHOICE is (B) 21.99 m

To explain I would say: The area of the sector = \(\frac {x^{\circ }}{360^{\circ }}\) × πr^2

= \(\frac {70^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 6^2

= 21.99 m

The correct ANSWER is (c) √0.63 m

The explanation is: The AREA of the CIRCLE (A) = πr^2

2 = \(\frac {22}{7}\) × r^2

r^2 = \(\frac {7}{22}\) × 2

r = √0.63 m

Correct option is (b) 2.74 m

For explanation: The area of the circle (A) = πr^2

6 = \(\frac {22}{7}\) × r^2

r^2 = 1.90

r = √1.90

r = 1.37 m

Diameter of the circle = 2 × RADIUS

= 2 × 1.37

= 2.74 m

Correct choice is (a) 2

Explanation: A circle CONTAINS TWO sectors. The sector having a LARGER area is called a major sector and the sector having a smaller area is called a MINOR sector.

The correct option is (b) 10.90 cm

For explanation: The area of the sector = \(\FRAC {x^{\circ }}{360^{\circ }}\) × πr^2

= \(\frac {50^{\circ }}{360^{\circ }} \times \frac {22}{7}\) × 5^2

= 10.90 cm

The correct ANSWER is (b) True

The best I can explain: The PATH that surrounds the OUTLINE of a two-dimensional SHAPE is CALLED the perimeter. The perimeter of a circle is also called the circumference.

Correct choice is (d) 70 CM

Explanation: The CIRCUMFERENCE of the circle = \(\FRAC {11}{5}\)m

2πr = \(\frac {11}{5}\)m

πd = \(\frac {11}{5}\)m(∵ Diameter = 2 × radius)

d = \(\frac {11}{5} \TIMES \frac {7}{22}\)m

d = 0.7 m

d = 0.7 × 100 cm

d = 70 cm

The CORRECT ANSWER is (a) False

Easiest EXPLANATION: A segment is a part of a circle that is OBTAINED by subtracting the triangle from the sector whereas, a sector is part of a circle that is enclosed by two RADII and an arc.