2019 · Q99
Consider the following for the next two (02) items:
The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm.
If S is the sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S - 3V) equal to?
Elementary MathematicsMensuration
- A572 cm³
- B728 cm³
- C1144 cm³
- DNone of the above
Explanation
l^3+b^3+h^3 − 3lbh = (l+b+h)((l^2+b^2+h^2) − (lb+bh+hl)). From (l+b+h)^2 = l^2+b^2+h^2 + 2(lb+bh+hl): 484 = 196 + 2(lb+bh+hl), so lb+bh+hl = 144. Hence S−3V = 22×(196−144) = 22×52 = 1144 cm^3.