Grade 10 : Mathematics - 11. Area Circles (Set 4)

Question 1

Find the area of a sector of a circle with radius 14 cmand a central angle of$60^\circ$.

Accepted Answer

B) $\frac{308}{3}cm^2$

Answer

A) $\frac{154}{3}cm^2$

Answer

C) $\frac{616}{3}cm^2$

Answer

D) $154cm^2$

Question 2

A circular track surrounds a circular park. The outer radius of the track is 21 mand the inner radius is14 m.

Calculate the surface area of the track.

Accepted Answer

A) $770m^2$

Answer

B) $616m^2$

Answer

C) $840m^2$

Answer

D) $539m^2$

Question 3

What is the perimeter of a sector of a circle with radius 7 cmand a central angle of$90^\circ$?

Accepted Answer

C) 25 cm

Answer

A) 11 cm

Answer

B) 18 cm

Answer

D) 32 cm

Question 4

A circle has a radius of 12 cm. Find the area of the minor segment formed by a central angle of $90^\circ$. (Take $\pi = 3.14$)

Accepted Answer

B) $41.04cm^2$

Answer

A) $24.84cm^2$

Answer

C) $56.16cm^2$

Answer

D) $72.00cm^2$

Question 5

If the ratio of the circumferences of two circles is $3:4$, what is the ratio of their respective areas?

Accepted Answer

B) $9:16$

Answer

A) $3:4$

Answer

C) $27:64$

Answer

D) $81:256$

Question 6

A square is inscribed inside a circle of radius 7 cm. Find the area of the region inside the circle but outside the square.

Accepted Answer

B) $56cm^2$

Answer

A) $42cm^2$

Answer

C) $70cm^2$

Answer

D) $84cm^2$

Question 7

The minute hand of a wall clock is 14 cmlong. Find the area swept by the minute hand in15 minutes.

Accepted Answer

B) $154cm^2$

Answer

A) $77cm^2$

Answer

C) $308cm^2$

Answer

D) $616cm^2$

Question 8

Two concentric circles have radii 10 cmand6 cm. Find the area of the ring bounded between these two concentric circles.

Accepted Answer

C) $64\picm^2$

Answer

A) $36\picm^2$

Answer

B) $48\picm^2$

Answer

D) $100\picm^2$

Question 9

A wire when bent in the form of a square encloses an area of $484cm^2$. If the same wire is reshaped to form a circle, what will be the area enclosed by the circle?

Accepted Answer

C) $616cm^2$

Answer

A) $484cm^2$

Answer

B) $528cm^2$

Answer

D) $704cm^2$

Question 10

A car wheel has a diameter of 70 cm. How many complete revolutions does each wheel make in 10 minuteswhen traveling at a constant speed of66 km/h?

Accepted Answer

C) 5000

Answer

A) 4000

Answer

B) 4500

Answer

D) 5500

Question 11

An equilateral triangle is inscribed in a circle of radius 6 cm. Find the area of the minor segment subtended by one side of the triangle. (Take $\sqrt{3} = 1.73$, $\pi = 3.14$)

Accepted Answer

B) $22.11cm^2$

Answer

A) $18.84cm^2$

Answer

C) $25.41cm^2$

Answer

D) $31.14cm^2$

Question 12

Three identical coins each of radius 3.5 cmare placed on a table such that each coin touches the other two. Find the area of the region enclosed between them. (Take$\sqrt{3} = 1.732$, $\pi = \frac{22}{7}$)

Accepted Answer

A) $1.97cm^2$

Answer

B) $2.45cm^2$

Answer

C) $3.14cm^2$

Answer

D) $4.22cm^2$

Question 13

Four equal circles of radius 7 cmeach touch externally such that their centers form a square. What is the area of the region bounded between the four circles?

Accepted Answer

C) $42cm^2$

Answer

A) $28cm^2$

Answer

B) $36cm^2$

Answer

D) $56cm^2$

Question 14

Sector ID	Radius ($r$)	Central Angle ($ heta$)
Sector A	21 cm	$120^\circ$
Sector B	28 cm	$45^\circ$

Based on the table above, calculate the difference between the area of Sector A and the area of Sector B.

Accepted Answer

B) $154cm^2$

Answer

A) $124cm^2$

Answer

C) $176cm^2$

Answer

D) $208cm^2$

Question 15

A square tablecloth has side length 28 cm. Four quarter-circle designs of radius 14 cmare printed at the four corners of the tablecloth.

Find the area of the unprinted center region of the tablecloth.

Accepted Answer

B) $168cm^2$

Answer

A) $144cm^2$

Answer

C) $196cm^2$

Answer

D) $212cm^2$

Question 16

A circular garden of radius 21 mis surrounded by a continuous circular concrete pathway of width7 m. The maintenance team charges ₹50 per square meter to pave the pathway.

Calculate the total cost of paving the pathway.

Accepted Answer

B) ₹53,900

Answer

A) ₹48,400

Answer

C) ₹57,200

Answer

D) ₹61,600

Question 17

If the perimeter and the area of a circle are numerically equal, what is the radius of the circle?

Accepted Answer

A) 2 units

Answer

B) $\pi	ext{ units}$

Answer

C) 4 units

Answer

D) 7 units

Question 18

Statement I: The area of a sector of angle $ heta$(in degrees) of a circle of radius$r$ is $\frac{ heta}{360^\circ} imes \pi r^2$.

Statement II: The length of an arc of a sector of angle $ heta$(in degrees) of a circle of radius$r$ is $\frac{ heta}{180^\circ} imes \pi r$.

Which of the following options correctly evaluates the statements above?

Accepted Answer

A) Both Statement I and Statement II are true.

Answer

B) Statement I is true, but Statement II is false.

Answer

C) Statement I is false, but Statement II is true.

Answer

D) Both Statement I and Statement II are false.

Question 19

A circular brooch is made with silver wire in the form of a circle with a diameter of 35 mm. The wire is also used in making 5diameters which divide the circle into10equal sectors.

Find the total length of silver wire required to construct the brooch.

Accepted Answer

B) 285 mm

Answer

A) 245 mm

Answer

C) 310 mm

Answer

D) 350 mm

Question 20

For the circular brooch described above (diameter 35 mmdivided into10equal sectors), what is the area of each sector?

Accepted Answer

C) $\frac{385}{4}	ext{ mm}^2$

Answer

A) $\frac{185}{4}	ext{ mm}^2$

Answer

B) $\frac{275}{4}	ext{ mm}^2$

Answer

D) $\frac{455}{4}	ext{ mm}^2$

Set 4Grade 10 : Mathematics - Area Circles

Grade 10 : Mathematics - Area Circles

Examination Instructions:

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Set 4Grade 10 : Mathematics - Area Circles

Grade 10 : Mathematics - Area Circles

Examination Instructions:

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Set 4Grade 10 : Mathematics - Area Circles

Grade 10 : Mathematics - Area Circles

Examination Instructions:

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Set 4Grade 10 : Mathematics - Area Circles

Grade 10 : Mathematics - Area Circles

Examination Instructions:

Share This Quiz

Discussion 0

Rating & Discussion Locked

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