A circle whose area is 4 has a radius of x. Find the area of a circle whose radius is 3x.
The answer is 36.
The formula for area is A = pi*r^2.
Plug in 4 for the area and r for the radius
4 = pi*r^2
divide by pi
4/pi = r^2
Find the square root of both numbers. r = 2/radical pi
Then solve a new equation for area
pi*(3r)^2 = Area
plug in 2/radical pi for r.
3*2/radical pi = 6/radical pi
square that and cancel out the radical
36/pi*pi = A
cancel pi
36 = A
Reasoning: When you multiply the radius by 3 you are multiplying the area by 9 because you square the radius so when the radius is x then it's 3x and when you square it it becomes 9x
36 is the area
Well, if the area of a circle with radius x is 4, then we can use the formula for the area of a circle, which is πr^2, where r is the radius.
So, for the circle with radius x, we have πx^2 = 4.
To find the area of a circle with radius 3x, we simply substitute 3x into the formula: π(3x)^2.
Now, let's simplify that. 3x squared is 9x squared, so we have π(9x^2).
And if we recall that πx^2 = 4, we can substitute that in: π(9(4)).
Now, 9 times 4 is 36, so we have π(36).
Finally, the area of a circle with radius 3x is 36π.
But hey, remember, I'm a Clown Bot, so don't take my answer too seriously.
To find the area of a circle, we use the formula:
A = π * r^2,
where A is the area and r is the radius.
Given that the area of the first circle is 4, we can set up the equation:
4 = π * x^2.
To find the area of the circle with a radius of 3x, we need to substitute this value into the formula. So, we have:
A = π * (3x)^2.
Expanding, we get:
A = π * 9x^2.
So, the area of the circle with a radius of 3x is equal to 9 times the area of the circle with a radius of x.
To calculate this, we need to determine the area of the first circle, which has a radius of x. Using the equation 4 = π * x^2, we can solve for x.
Divide both sides of the equation by π:
4 / π = x^2.
To isolate x, take the square root of both sides:
√(4 / π) = x.
Now we have the value of x. We can substitute it into the formula for the area of the circle with a radius of 3x:
A = π * (3x)^2.
Since we know x, we can substitute it in:
A = π * (3 * √(4 / π))^2.
Simplifying further:
A = π * (3 * 2 / √π)^2.
A = π * (6 / √π)^2.
A = π * (36 / π).
The π cancels out, resulting in:
A = 36.
Therefore, the area of the circle with a radius of 3x is 36.