Question

the difference between the circumference and radius of a circle is 37. The area of the circle is:
a) 111 cm²
b) 184 cm²
c) 154 cm²
d) 259 cm²
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Answer 1

Answer:

OPTION C (154 cm^2)

is correct answer

Step-by-step explanation:

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Answer 2

◑ Given ◐

• The difference between the circumference and radius of a circle is 37.

◑ To find ◐

• Area of circle

◑ Solution ◐

The difference between the circumference and radius of a circle is 37cm

• As we know that

$\\\quad{\red\bigstar}\:{\underline{\tt {\purple{Circumference\:of\:Circle=2\pi r}}}}$

• It is given that the difference between 2πr & r is 37 cm

$\\\bold\dag\:{\underline{\sf{\pink{Circumference\:of\:circle - radius}}}}$

$\implies\sf 2\pi r - r = 37$

• Put the value of π

$\\\implies\sf 2\times \dfrac{22}{7} \times r - r = 37$

$\implies\sf \dfrac{44r}{7} - r = 37$

$\implies\sf \dfrac{44r - 7r}{7} = 37$

$\implies\sf \dfrac{44r - 7r}{7} = 37$

$\implies\sf \dfrac{37r}{7} = 37$

• Cross multiplication

$\\\\\implies\sf 37r = 7 \times 37$

$\implies\sf r = \dfrac{37 \times 7}{37}$

$\therefore{\underline{\boxed{\sf{\blue{Radius = 7cm}}}}}$

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• Now we have to find out area of circle

$\\\qquad \: \: {\red\bigstar}\:{\underline{\tt{\purple{ Area\:of\:Circle=\pi r^2}}}}$

• Put the value of radius

$\\\implies\sf \dfrac{22}{7}\times 7 \times 7$

$\implies\sf 22 \times 7$

$\implies\sf 154cm^2$

$\therefore{\underline{\boxed{\sf{\blue{Area\:of\:circle\:is\:154cm^2}}}}}$

• (c) is the correct option

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