guerrero wrote:
"The area of the circle is increased by 800%, thus the area is increased 9 times.
The area of a circle it proportional to the square of the diameter (area=pi d^2 / 4), therefore the diameter must increase 3 times (diameter increase 3 times = area increase 9 times), which is increase by 200%."
That's a legitimate/valid solution, but potentially hard to conceptualize for some students. So, I like the idea of playing it safe and doing some testing.
For this question, it's not a bad idea to start testing cases, beginning with the middle (C)
C) 300% increase
Let's say the original circle has radius 1 (i.e., diameter = 2)
The area of this circle is
pi
If the diameter increases 300%, then the new diameter is 8, which means the radius = 4
If the radius of the enlarged circle is 4, the area is
16(pi)
An area increase from
pi to
16(pi) represents a 1500% increase.
We want an 800% increase.
So C is not the correct answer. In fact, we're looking for a smaller increase. So, let's try . . .
B) 200% increase
Let's say the original circle has radius 1 (i.e., diameter = 2)
The area of this circle is
pi
If the diameter increases 200%, then the new diameter is 6, which means the radius = 3
If the radius of the enlarged circle is 3, the area is
9(pi)
An area increase from
pi to
9(pi) represents an 800% increase.
BINGO!
The answer is
B
Cheers,
Brent
