If you fit the cone with the largest possible surface area (lateral area plus area of base) into a sphere, what percent of the volume of the sphere is occupied by the cone?
I did the r^2=R^2-(h-R)^2 insert but there’s an extra R or variable that didn’t clear at the finish. The answer is 1033/4096 + 33/4096sqrt(17) = 0.2854 but the algebra became long and my answer is not matching because there’s like a locked square root that’s not factoring out properly and I’m tired to do the long multiplication. Could a g show me?
I did the r^2=R^2-(h-R)^2 insert but there’s an extra R or variable that didn’t clear at the finish. The answer is 1033/4096 + 33/4096sqrt(17) = 0.2854 but the algebra became long and my answer is not matching because there’s like a locked square root that’s not factoring out properly and I’m tired to do the long multiplication. Could a g show me?
