The area of a quadrant of a circle whose circumference is 25 cm is :
(a) 24 cm²
(b) 28 cm²
(c) 32.5 cm²
(d) 38,5 cm²
Answers
Answer:
d) 38.5cm² will be the answer.
Check this question solution by clicking the pic.
Refer to the attached image. You can see a quadrant of a circle is marked clearly.
Step-by-step explanation:
Let the radius of the circle be r. Then the circumference of one quadrant be (2πr/4 + r + r) cm = (πr + 4r)/2 cm.
By the given condition,
(πr + 4r)/2 = 25
⇒ πr + 4r = 50
⇒ 22r/7 + 4r = 50, since π = 22/7
⇒ (22r + 28r)/7 = 50
⇒ 50r = 50 × 7
⇒ r = 7
Then the radius of the circle is 7 cm.
Now the area of one quadrant of the circle
= πr² / 4 cm²
= 22/7 × (7)² × 1/4 cm²
= (22 × 49)/(7 × 4) cm²
= 38.5 cm²
Answer: Option (d) 38.5 cm²
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