Question

A circle has an area of 25 pi cm squared. If a circle is drawn within that circle with a diameter equal to the radius of the first circle what is the area of the second circle?
A. 2 1/2 PI
B.4 1/4 PI
C. 5 1/4 PI
D.6 1/4 PI
E.7 1/2

Answer 1

area = pi * r². Your circle has 25pi = pi * squareroot(25) = pi * 5, so r =5.

Diameter is 2*r, so the diameter of the second circle must be 5, then the radius of the second circle must be 2*r=5, r = 5/2 = 2 ½.

Now the area of the 2nd circle is: pi * r² = pi * (2½)² = pi * 4 1/4. Your answer is B.

Answer 2

D.

Let \[r_1 \] be the radius of the first circle and
\[r_2\] be the radius of that of the second.

For the first circle,\[\pi (r_{1})^2 =25\]
The second circle's radius is half the radius of the first one.\[\pi(\frac{1}{2}r)^2=x\]
Simplifying, we get \[\pi \frac{1}{4}r^2=x\]
But according to the given, \[\pi r^2 =25\]
So, \[25 (\frac{1}{4})=x=6\frac{1}{4}\]

Answer 3

BTW, let x be the area of the second circle.

Answer 4

you made a mistake there jyqft, the first circle has \[25\pi = \pi * (r_{1})^2\]