Each of four circles has a radius of 4 inches. A larger circle has an area equal to the total area of the four smaller circles. What is the length of the radius, in inches, of the larger circle?
I need to find the radius of the larger circle, which I'll call R. I know that the area of a circle is given by the formula A = pi * r^2, where r is the radius and pi is a constant. So, the area of each of the smaller circles is pi * 4^2 = 16 * pi. The total area of the four smaller circles is 4 * 16 * pi = 64 * pi. This is also the area of the larger circle, so I can set it equal to pi * R^2 and solve for R. pi * R^2 = 64 * pi. Dividing both sides by pi, I get R^2 = 64. Taking the square root of both sides, I get R = 8. So, the radius of the larger circle is 8 inches. 