Question

The surface areas of the six faces of a rectangular solid are 16, 16, 32, 32, 72 and 72 sq cm. The volume of the solid (in cubic cm) is
a) 192
b) 384
c) 480
d) 2592

Answer 1

Since, the solid has rectangular faces
So, we have
$l\times b=16$ ..... (i)
$b\times h=32$ ...... (ii)
$l\times h=72$ ....... (iii)
where l, b and h are the length, breadth and height respectively of the solid.
On multiplying equations (i), (ii) and (iii), we get
$l\times b\times b\times h\times l\times h=16\times 32\times 72\Rightarrow l^2\times b^2\times h^2=36,864\Rightarrow (lbh{)}^2=36,864\therefore lbh=192$
Hence, the volume of the solid is 192 cu cm.