Case Study Chapter 11 Areas related to Circles Mathematics

l. Read the following and answer The art department of a school prepared circular hanging for the annual function of the school. The circle with diameter 42 cm was placed at the bottom and the size of the middle circle was half the size of the bottom one and the smallest circle was half the size of the middle circle.

Question. The area of the bottom circular region that is visible is
(a) 1323/2 πcm²
(b) 1323/4 πcm ²
(c) 245π cm²
(d) 340π cm²

Answer: B

Question. The ratio of the areas of the three circles, starting from the bottom circle is
(a) 16: 4 : 1
(b) 4 : 2 : 1
(c) 1: 2 : 4
(d) 1 : 4 : 16

Answer: A

Question. A colourful tape was used to decorate the boundary of the bottom circle. The length of tape used is
(a) 42 cm
(b) 42π cm
(c) 21 cm
(d) 21π cm

Answer: B

Question. The radius of the smallest circle is
(a) 7 cm
(b) 14 cm
(c) 10.5 cm
(d) 5.25 cm

Answer: D

Question. The area of the middle circle is
(a) 154 cm²
(b) 616 cm²
(c) 346.5 cm²
(d) 1386 cm²

Answer: C

ll. Read the following and answer Gauri got her wall painted in a different manner. The whole wall was painted pink, leaving a circular portion of diameter 4.2m. In this circle, she asked the painter to paint a beautiful scenery in one half of it by drawing a full size triangle possible (as shown in the figure). In the other half of the circle, she drew the largest circle possible and pasted some of her pictures. The remaining part of the big circle was filled with dotted design.

Question. The area of the wall that is not painted pink is given by

(a) (96 – 4.41π) m²
(b) (40 – 4.41π) m²
(c) (96 – 17.64π) m²
(d) (40 – 17.641π) m²

Answer: A

Question. The area of the dotted design is approximately
(a) 10 m²
(b) 6 m²
(c) 9 m²
(d) 8 m²

Answer: B

Question. The cost of designing the whole circular region at the rate of ` 80 per m² is
(a) ₹ 4,435.2
(b) ₹ 110.88
(c) ₹ 1,108.80
(d) ₹ 346.50

Answer: C

Question. The area of the triangular region is
(a) 4.41 m²
(b) 8.82 m²
(c) 2.205 m²
(d) 17.64 m²

Answer: A

Question. The radius of the circle allotted for her pictures is
(a) 4.2 m
(b) 2.1 m
(c) 1.05m
(d) cannot be determined

Answer: C

lll. Read the following and answer Raghav was standing outside his home. He then tried to find how many times does the wheel of the car move in a certain time.

Question. The number of revolutions made by the wheel in eleven minutes is
(a) 31
(b) 32
(c) 18
(d) 25

Answer: A

Question. If the circumference and the area of a circle are numerically equal, then diameter of the circle is
(a) 2 units
(b) 4 units
(c) 6 units
(d) 1 unit

Answer: B

Question. The area of a circular ring formed by the circles of radii a and b respectively is given by
(a) 2π (a – b)
(b) 2π (a² – b²)
(c) π (a² – b²)
(d) π (a² + b²)

Answer: C

Question. Raghav measured the diameter of his car’s wheel and found it to be 84 cm. The distance travelled by the wheel in one revolution is
(a) 84π cm
(b) 42π cm
(c) 21π cm
(d) 176π cm

Answer: A

Question. He observed that an average speed of car in front of his house is 45 km/h. The distance travelled in 1 minute is
(a) 450 m
(b) 750 m
(c) 500 m
(d) 760 m

Answer: B

lV. Read the following and answer A horse and an ox are tied to a peg at opposite corners of a rectangular field of dimensions 35 m × 20 m by ropes of length 5 m and 10 m respectively. (use π = 3.14)

Question. The area of the field left to be grazed is
(a) 700 – 125π /2 m²
(b) 700 – 125π/4 m² 
(c) 110 – 125π/2 m² 
(d) 110 – 125π/4 m² 

Answer: B

Question. If the rope to which horse is tied would have been 8 m long, then the increase in the grazing area is given by
(a) 39/4 π m²
(b) 35/4 π m²
(c) 37/2 π m²
(d) 35/2 π m²

Answer: A

Question. The area of a sector of a circle bounded by an arc of length 5π cm is equal to 20r cm2, then its radius is
(a) 12 cm
(b) 16 cm
(c) 8 cm
(d) 10 cm

Answer: C

Question. The area of the field that the horse can graze is given by   
(a) 25π m²
(b) 10π m²
(c) 25/2 π m²
(d) 25/4 π m²

Answer: D

Question. The area of the field the ox can graze is
(a) 78.5 m²
(b) 157 m²
(c) 314 m²
(d) 62.8 m²

Answer: A