Question

The square of radius of a circle whose area is equal to the difference of the areas of the two circles of radii 5 cm and 3 cm is

Answer 1

Correct Question :

Find radius of a circle whose area is equal to the difference of the areas of the two circles of radii 5 cm and 3 cm is

Given :

• Radius of two circles is 5 cm and 3 cm

To Find :

• Radius of new circle =??

Formula used :

${\underline{ \boxed{\bold {\pink{ Area\:of\:circle=\pi\:r^2}}}}} \: \: \: \: \: \bigstar$

Solution :

$\sf{ : \implies \pi\:(r^1)^2-\pi\:(r^2)^2=\pi\:r^2}$

$\sf{:\implies \pi\:(5)^2-\pi\:(3)^2=\pi\:r^2}$

$\sf{:\implies \pi(5^2-3^2)=\pi\:r^2}$

$\sf{:\implies \pi(25-9)=\pi\:r^2}$

$\sf{:\implies \pi(16)=\pi\:r^2}$

$\sf{:\implies r^2=16}$

$\sf{:\implies r=\sqrt{16}}$

$\sf{:\implies r=4 cm}$

Hence ,

The radius new circle = 4cm

Answer 2

Given: The area of a circle is equal to the difference of the areas of the two circles of radii 5 cm and 3 cm.

To find: Square of the radius of the circle

Explanation: Area of a circle is given by thr formula:

$\pi {r}^{2}$

where r is the radius of the circle

Area of circle with radius 5 units

=$\pi \times {5}^{2}$

= 25π cm^2

Area of circle with radius 3 units

=$\pi \times {3}^{2}$

=9π cm^2

Difference of areas

= 25π -9 π

= 16 π cm^2

Let the radius of the circle whose area is 16π be r.

Then,

=>$\pi {r}^{2} = 16\pi$

=>${r}^{2} = 16$

=>r = 4 cm

Therefore, the radius of the circle is 4 cm.

The square of radius of this circle is:

${4}^{2} = 16$

Therefore, the square of the radius of the circle whose area is equal to the difference of the areas of the two circles of radii 3 cm and 5 cm is 16.