June 2023
Problem of the Month

Box in a Sphere
Submitted by Brijesh Dave

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:

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)

Send any comments or questions to: David Pleacher