Question

find the circumference of a circle whose area is 16 times the area of the circle with diameter 7 cm

Answer 1

Answer:

Step-by-step explanation:

Given that, Area of circle is 16 times the area of circle with Diameter 7 cm.

We must find the Circumference of the circle.

Let's find the area of circle with diameter 7 cm

⇒ Area = πr²

⇒ Area = 22 / 7 × 49 = 22 × 7 = 154 cm²

We know that 16 times this area is the area of the unknown circle.

Hence Area of Unknown circle is = 16 × 154 = 2464 cm²

⇒ πr² = 2464

⇒ r² = 2464 / π = 2464 / ( 22/7 ) = 784 cm²

⇒ r = √784 = 28

Hence Circumference = 2πr = 2 × 22/7 × 28 = 2 × 22 × 4 = 176 cm.

Hope it helped !!

Thanks !!

Answer 2

Solution:

Given,

The Area of circle is 16 times the area of circle with Diameter 7 cm.

Now,

Finding the area of circle ,

⇒ Area = πr²

⇒ Area = 22 / 7 × 49

= 22 × 7

= 154 cm²

We have, 16 times the area is the area of the unknown circle.

Therefore, Area of Unknown circle is:

= 16 × 154 = 2464 cm²

Again,

⇒ πr² = 2464

⇒ r² = 2464 / π = 2464 / ( 22/7 ) = 784 cm²

⇒ r = √784 = 28

Therefore, Circumference = 2πr

= 2 × 22/7 × 28

= 2 × 22 × 4

= 176 cm.

Hope It Helps !