Question

The diameters of three circles are in the ratio $3:5:6$ . If the sum of the circumferences of these circles be $308cm$; find the difference between the areas of the largest and the smallest of these circles.

• A. $1039.5c{m}^2$
• B. $1339.5c{m}^2$
• C. $1239.5c{m}^2$
• D. $1139.5c{m}^2$

Answer 1

The correct option is A $1039.5c{m}^2$

Given,

Diameter of three circle=$3:5:6$

Sum of the circumference=$308cm$

Let the diameter of the circles be $3x,5x,6x$

Now, $\pi \left(3x\right)+\pi \left(5x\right)+\pi \left(6x\right)=308$

$=>14x\pi =308$

$=>x=\frac{308}{2\times 22}$

$=>x=7$

Therefore, diameter of the largest side=$6\times 7$=$42$

Radius of largest circle=$\frac{6\times 7}{2}$=$21$

Diameter of the smallest circle=$3x$=$3\times 7$ =$21$

Radius of smallest circle=$\frac{3\times 7}{2}$=$10.5$

Difference of areas of largest and smallest of the circles=$\pi (21{)}^2-(\pi (10.5{)}^2$

=$1039.5c{m}^2$