A circle has a radius of 12 cm . If the area is multiplied by 25 ,
what happens to the radius?

Question

A circle has a radius of 12 cm . If the area is multiplied by 25 , what happens to the radius?

UpStudy AI · Accepted Answer

1. The area of a circle is given by the formula  
   $$
   A = \pi r^2.
   $$

2. For the original circle with radius $$ r = 12 $$ cm, the area is  
   $$
   A = \pi (12)^2 = 144\pi.
   $$

3. When the area is multiplied by 25, the new area becomes  
   $$
   A' = 25 \times 144\pi = 3600\pi.
   $$

4. Let the new radius be $$ r' $$. Using the area formula for the new circle, we have  
   $$
   \pi (r')^2 = 3600\pi.
   $$
   Dividing both sides by $$\pi$$, we get  
   $$
   (r')^2 = 3600.
   $$

5. Taking the square root of both sides, we find  
   $$
   r' = \sqrt{3600} = 60 \text{ cm}.
   $$

Thus, when the area is multiplied by 25, the radius increases from 12 cm to 60 cm.
When the area of the circle is multiplied by 25, the radius increases from 12 cm to 60 cm.

A circle has a radius of 12 cm . If the area is multiplied by 25 ,
what happens to the radius?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Geometry Questions