find the circumference of the circle whose area is 16 times the area of circle with diameter 7 cm
Answers
Answer:
Required circumference is 88 cm.
Step-by-step explanation:
First, finding the area of the circle whose diameter is 7 cm.
From the properties of circle : -
- Area of circle = πr^2 [ where r is the radius ]
- Circumference of circle = 2πr [ where r is the radius ]
Thus,
= > Area of circle with diameter of 7 cm
= > πr^2
= > π x ( diameter / 2 )^2 [ radius = diameter / 2 ]
= > 22 / 7 x ( 7 / 2 cm )^2
= > 22 / 7 x 7 / 2 x 7 / 2 cm^2
= > 11 x 7 / 2 cm^2
= > 77 / 2 cm^2
Then, finding the radius of the circle whose area is 16 times the area of the circle with diameter of 7 cm.
= > Area of the required circle = 16 x ( 77 / 2 ) cm^2
= > π( radius )^2 = 16 x 77 / 2 cm^2
= > 22 / 7 x radius^2 = 16 x 77 / 2 cm^2
= > radius^2 = 7 / 22 x 16 x 77 / 2 cm^2
= > radius^2 = 196 cm^2
= > radius = 14 cm
Hence,
= > Circumference of the required circle = 2 x 22 / 7 x 14 cm
= > Circumference of the required circle = 88 cm
Hence the required circumference is 88 cm.