Question

the circumference of two circles are in ratio 3:4 .find ratio of their areas . explain it steps with answers. fast .

Answer 1

Solution is in the attachment..

Answer 2

Answer:

9:16

Step-by-step explanation:

$\text{Ratio of circumferences = 3:4}\\\\\text{Let circumference of first circle be 3x and of the second circle be 4x.}\\\\\text{Circumference of circle is 2 \pi r , where r is the radius.}\\\\\text{Let radius of smaller circle be r and of the larger circle be R.}\\\\\text{Circumference of small circle = 2 \pi r }\\\\\text{And, Circumference of larger circle = 2 \pi R }\\\\\text{Ratio of circumferences = 2 \pi r \div 2 \pi R = r \div R \: or \: r:R }$

$\text{But, ratio of circumferences = 3:4 or 3x:4x}\\\\r:R = 3x:4x\\\\\implies r = 3x \: and \: R = 4x\\\\\text{Area of smaller circle = \pi r^2 = \pi \times (3x)^2 = 9 \pi x^2 }\\\\\text{Area of larger circle = \pi R^2 = \pi \times (4x)^2 = 16 \pi x^2 }\\\\\text{Ratio of areas = 9 \pi x^2 \div 16 \pi x^2 = 9 \div 16 \: or \: 9:16 }\\\\\therefore \text{Ratio of areas} = \large \underline{\boxed{\boxed{\bold{9:16}}}}$

Hope it helps.