Question

Priya drew a circle whose area is 25 cm. Dan drew a circle whose diameter is 4 times the radius of Priya's circle. How many times greater is the area of Dan's
circle?

Answer 1

Answer:

400

Step-by-step explanation:

first work out the radius of priya's circle with the equation a = $\pi r^{2}$

$25 = \pi r^{2}$

$\frac{25}{\pi } = r^{2}$

$r = \sqrt{\frac{25}{\pi } }$

we know the diameter of a circle is 2 times the radius so the diameter of priya's circle is 2x$\sqrt{\frac{25}{\pi } }$

this means that if the diameter of dan's circle is 4 times bigger it must be

8x$\sqrt{\frac{25}{\pi } }$

to find the radius of dan's circle we divide the diameter by to 2 to give

4x $\sqrt{\frac{25}{\pi } }$

then use the a=$\pi r^{2}$ equation again

$a= (4 \sqrt{\frac{25}{\pi } })^{2} \pi$

which equals 400

hope that helped