Question

Two circles have the same center. The radius x of the smaller circle is 5 units less than the radius of the larger circle. How many more square units does the larger circle have? A) -25pi B) (10x+25)pi C)(x*2 +10x+25)pi D)25pi

Answer 1

B

Explanation:

The radius of the larger circle is x+5 (5 units larger than the radius of the smaller circle). Since the area of a circle is A=(r^2)(pi), we know that the area of the larger circle is:

A=((x+5)^2)(pi)

A=(x^2+10x+25)(pi)

NOTE: This is only the area of the larger circle, the question is asking how many more square units the larger circle has. In other words, the question is asking what the area of the space between the two circles is.

So, next we need the area of the smaller circle:

A=(x^2)(pi)

Therefore, the area between the two circles:

(x^2+10x+25)(pi)-(x^2)(pi)

=(10x+25)(pi)

B) (10x+25)pi

Answer 2

d) 25pi

Explanation:

Square units imply area.

The area of a circle is:

A = pi * r * r

Difference in radius = 5

pi * 5 * 5 = 25pi

So the answer is d.