If the area of a circle is twice the area of a triangle whose base is 4 pi and whose altitude is 4, the radius of the circle equals
a. square root 32
b. 2
c. 4
d. 8
e. 32
please answer and explain
√(2* 1/2 * 4pi * 4/pi) = 2√2 = 4
oops. 2√2 left over from when I only did 1 times the area of the triangle. Ignore it.
To solve this problem, we need to set up an equation based on the given information and then solve for the radius of the circle.
Let's start with the formula for the area of a circle: A = πr^2, where A is the area and r is the radius of the circle.
The area of the circle is given as twice the area of a triangle.
So, let's find the area of the triangle.
The formula for the area of a triangle is: A = (1/2) * base * height.
In this case, the base of the triangle is given as 4π and the height (or altitude) is given as 4. Therefore, the area of the triangle is:
A_triangle = (1/2) * (4π) * 4
A_triangle = 8π
Now, according to the problem statement, the area of the circle is twice the area of the triangle. Therefore, we can write the equation as:
A_circle = 2 * A_triangle
Substituting the values we have:
πr^2 = 2 * 8π
πr^2 = 16π
We can cancel out the π on both sides of the equation, giving us:
r^2 = 16
Now, we can solve for r by taking the square root of both sides of the equation:
r = √16
Simplifying the square root of 16, we get:
r = 4
Therefore, the radius of the circle is 4.
Hence, the correct option is c) 4.