Answer:
400
Step-by-step explanation:
first work out the radius of priya's circle with the equation a = [tex]\pi r^{2}[/tex]
[tex]25 = \pi r^{2}[/tex]
[tex]\frac{25}{\pi } = r^{2}[/tex]
[tex]r = \sqrt{\frac{25}{\pi } }[/tex]
we know the diameter of a circle is 2 times the radius so the diameter of priya's circle is 2x[tex]\sqrt{\frac{25}{\pi } }[/tex]
this means that if the diameter of dan's circle is 4 times bigger it must be
8x[tex]\sqrt{\frac{25}{\pi } }[/tex]
to find the radius of dan's circle we divide the diameter by to 2 to give
4x [tex]\sqrt{\frac{25}{\pi } }[/tex]
then use the a=[tex]\pi r^{2}[/tex] equation again
[tex]a= (4 \sqrt{\frac{25}{\pi } })^{2} \pi[/tex]
which equals 400
hope that helped
