Area Related to Circle Test

Result

Area Related to Circle Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

Anu prepares two playgrounds for pets, one is circular and another is rectangular. The areas of the circular and rectangular playgrounds are 22,176 cm² and 55,440 cm², respectively. She wants to create a fence around the playgrounds. If the length of the rectangular playground is 13.86 m, then how much more wire does she have to buy for the rectangular playground than for the circular playground?

A
20.15 m

B
18.44 m

C
23.24 m

D
28.94 m

Solution

Area of the circular playground = πr²
22,176 = πr²

22,176 × 7/22 = r²
7056 = r²
r = 84 cm

Amount of wire used for the circular playground = Circumference of the circle = 2πr
= 2 × 22/7 × 84

= 528 cm --- (1)
13.86 m = 13.86 × 100 = 1386 cm
Area of the rectangular playground = l × b

55,440 = 1386 × b
55,440 ÷ 1386 = b
40 cm = b

Perimeter of the rectangle = 2(l + b)
= 2(1386 + 40)
= 2(1426)
= 2852 cm --- (2)

Length of the extra wire for rectangular playground = 2852 – 528 [from equations (1) and (2)] = 2324 cm
2324 cm = 2324 ÷ 100 = 23.24 m