Question

the difference between the circumference and radius of a circle is 111 cm then the area of a circle.
answer : 1386
need explanation​

Answer 1

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☆ Given :

circumference - radius = 111cm

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Procedure:

2πr - r = 111

▪︎ r(2π -1) = 111

▪︎ r = 111/(2π-1)

▪︎r = 111(2*22/7-1)

● r = 111( 44/7-1)

● r = 111( 37/7)

▪︎ r = 111* 7/37

▪︎ r = 3*7

r = 21 cm.

Diameter = 2 r

= 2*21 => 42 cm

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Area :

$\pi \times {r}^{2}$

$\frac{22}{7} \times 21 \times 21 \\ \\ = 22 \times 3 \times 21 \\ \\ </h3><h2>= <u>1386</u>$

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Answer 2

Answer- The above question is from the chapter 'Areas Related to Circles'.

Concepts used: 1) Circumference of circle = 2πr

2) Area of circle = πr²

Given question: The difference between the circumference and radius of a circle is 111 cm, then the area of a circle is ____ .

Solution: Let r be the radius of a circle.

2πr - r = 111 cm

r (2π - 1) = 111

r × $\dfrac{44 - 7}{7}$ = 111

r × 37 = 777

r = 777 ÷ 37

r = 21 cm

Area of circle = πr²

Area of circle = $\dfrac{22}{7}$ × 21 × 21

Area of circle = 22 × 3 × 21

Area of circle = 1386 cm²

∴ The difference between the circumference and radius of a circle is 111 cm, then the area of a circle is 1386 cm².