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Step-4

Title: Area of a circle

Grade: 8-a Lesson: S4-L4

Explanation: Let us verify the answer here with the steps.

Description:

Step	Type	Explanation	Answer
1	Problem	The circumference of a circle is 44 cm. Find the area(approximately) of the circle if the radius is 7 cm.
2	Hint	Formula used	\$"Area(A)" = \pi r^2\$
3	Step	Given that,	The circumference of the circle = 44 cm and The radius of the circle (r) = 7 cm
4	Hint	We know that, the circumference of a circle	= 2πr
5	Step	Therefore,	2πr = 44 cm ⇒ \$\pi r = \cancel(44)^22/\cancel2^1\$ ⇒ \$\pi r = 22\$ ⇒ \$r = 22/π cm\$
6	Step	Now,	Area = πr² ⇒ \$A = \pi (22/\pi)^2\$ ⇒ \$A = \cancel\pi^1 (484)/(\pi)^\cancel2\$ ⇒ \$A = (484)/\pi \$ ⇒ \$A = (484)/(3.14) \$ ⇒ \$A= 154.14 (cm^2)\$ (rounded to two decimal places)
7	Step	Therefore, the area of the circle is	154.14 cm².

Step

Type

Explanation

Answer

Problem

The circumference of a circle is 44 cm. Find the area(approximately) of the circle if the radius is 7 cm.

Hint

Formula used

\$"Area(A)" = \pi r^2\$

Step

Given that,

The circumference of the circle = 44 cm and

The radius of the circle (r) = 7 cm

Hint

We know that, the circumference of a circle

= 2πr

Step

Therefore,

2πr = 44 cm

⇒ \$\pi r = \cancel(44)^22/\cancel2^1\$

⇒ \$\pi r = 22\$

⇒ \$r = 22/π cm\$

Step

Now,

Area = πr²

⇒ \$A = \pi (22/\pi)^2\$

⇒ \$A = \cancel\pi^1 (484)/(\pi)^\cancel2\$

⇒ \$A = (484)/\pi \$

⇒ \$A = (484)/(3.14) \$

⇒ \$A= 154.14 (cm^2)\$ (rounded to two decimal places)

Step

Therefore, the area of the circle is

154.14 cm².