A rectangular box P is inscribed in a sphere of radius r.
The surface area of P is 384, and the sum of the lengths of its 12 edges is 112.
What is the value of r?



Solution to the Problem:


The radius r = 10.

Let the dimensions of Box P be l, w, and h.
Its surface area is 2lw + 2lh + 2wh = 384.
The the sum of all its edges is 4l + 4w + 4h = 112.
Therefore, l + w + h =28
The diameter of the sphere is the space diagonal of the prism:

So, the radius = 10.


Correctly solved by:

1. K. Sengupta Calcutta, India
2. Colin (Yowie) Bowey Beechworth, Victoria, Australia
3. Davit Banana Istanbul, Turkey
4. Kelly Stubblefield Mobile, Alabama
5. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
6. Seth Cohen Concord, New Hampshire
7. Rob Miles Northbrook, Illinois
8. Aariv (Courtney Teddy's student) Issaquah, Washington (5th Grade Clark Elementary)