The sum of the surface areas of two spheres is 12584 π sq. cm. The radius of the larger sphere is five times the radius of the smaller sphere. Find the diameter of the larger sphere.
110 cm
Let the smaller sphere's radius be r, so the larger sphere's radius is 5r.
Sum of surface areas: \(4\pi r^2 + 4\pi(5r)^2 = 12584\pi \Rightarrow 4r^2+100r^2 = 12584 \Rightarrow 104r^2=12584 \Rightarrow r^2=121 \Rightarrow r=11\).
Larger sphere's radius: \(5\times11 = 55\) cm, so its diameter is \(110\) cm.
Hence, the diameter of the larger sphere is 110 cm.
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