A rectangular box P is inscribed in a sphere of radius r cm. The surface area of P is 384 cm2. and the sum of the length of its 12 edges is 112 cm. Then r (in cm.) is equal to- एक आयताकार बाक्स P, एक r सेमी. त्रिज्या वाले गोले में खींचा जाता है। P का पृष्ठीय क्षेत्रफल 384 सेमी2. है और इसके 12 कोरो की लम्बाई का योग 112 सेमी. है, तो r (सेमी. में) बराबर है-

For a rectangular box with dimensions l, b, h: 4(l+b+h) = 112, so l+b+h = 28. Surface area: 2(lb+bh+lh) = 384. If edges are 8, 12, 16: sum = 28 ✓, surface area = 2(96+192+128) = 2(416) = 832 ✗. If edges are 8, 12, 8: surface area = 2(96+96+64) = 512 ✗. For a box inscribed in a sphere, the sphere's diameter equals the box's diagonal. With edges summing to 28 and surface area 384, the dimensions satisfy these conditions, giving a diagonal of 20, so radius r = 10.