Question

The figure shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in centimetre. Assume that all angles in figure are right angles.

• A. $180$ $c{m}^3$
• B. $108$ $c{m}^3$
• C. $188$ $c{m}^3$
• D. $118$ $c{m}^3$

Answer 1

The correct option is A $180$ $c{m}^3$

The image consists of two cuboids. When we subtract the volume of smaller cuboid from the larger cuboid, we will get the volume of the desired cuboid.

$volumeofcuboid=length\ast breadth\ast height$

Dimensions of larger cuboid

$length=4cm$

$breadth=9cm$

$height=9cm$

$volume=4\ast 9\ast 9=324$

Dimensions of smaller cuboid

$length=4cm$

$breadth=6cm$

$height=6cm$

$volume=4\ast 6\ast 6=144$

$volumeofdesiredcuboid=volumeoflargercuboid-volumeofsmallercuboid$

$volumeofdesiredcuboid=324-144=180c{m}^3$