Question

The radius of a circle with an area of 60 square centimeters is represented by the expression

60
centimeters. What is
T
another way of expressing the radius?
O 2 155
O 4.55
2157
4.5
T

Answer 1

we know that

area of the circle is equal to

A=pi* r^{2}A=pi∗r

2

solve for r

r= \sqrt{ \frac{A}{pi}}r=

pi

A

for A=60 cm^{2}60cm

2

r= \sqrt{ \frac{60}{pi}} cmr=

pi

60

cm

we know that

\begin{gathered} \sqrt{60} = \sqrt{ 2^{4}*3*5} \\ =2 \sqrt{15} \end{gathered}

60

=

2

4

∗3∗5

=2

15

so

\sqrt{ \frac{60}{pi}}=2 \sqrt{ \frac{15}{pi}}

pi

60

=2

pi

15

2 \sqrt{ \frac{15}{pi}}=2 \frac{ \sqrt{15}}{ \sqrt{pi}} * \frac{ \sqrt{pi}}{ \sqrt{pi}}2

pi

15

=2

pi

15

∗

pi

pi

=2 \frac{ \sqrt{15pi}}{pi} cm=2

pi

15pi

cm

the answer is

2 \frac{ \sqrt{15pi}}{pi} cm2

pi

15pi

cm