If S is sum of the cubes of the dimensions of the cuboid and V is its volume then what is S 3V equal...........

Quantitative Aptitude (CDS) Coordinate Geometry

Direction: 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 sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to?

572 cm³

728 cm³

1144 cm³

None of the above

छोटे Courses बड़े Results

Master Coordinate Geometry

Prepare through Micro-courses

Try Now

Explanation:

Let lengths, breadth and height of cuboid be l, b and h respectively
According to question
l+b+h = 22cm……(i)
and √(l²+b²+h²) = 14cm …..(ii)
S = l³+b³+h³ and V = lbh
S-3V = l³+b³+h³ - 3 lbh = (l+b+h)( l²+b²+h²-[lb+bh+lh])…(iii)
As we know Squaring eq (i) gives
l²+b²+h² + 2(lb+bh+lh) = 484
Substituting l²+b²+h² from eq (i)
2(lb+bh+lh) = 484-196 = 288 cm²
lb+bh+lh = 144 cm²
Putting this in eq (iii) we get
22(196-144) = 22*52 = 1144cm2