Question

Jack has a toy in which half of the cylindrical shape is surmounted on a cuboid as shown in the figure below.

Total volume of the given solid is

• A. $365.71c{m}^3$
• B. $302.855c{m}^3$
• C. $302.855c{m}^3$

Answer 1

The correct option is B $302.855c{m}^3$

Total volume of a given solid = Volume of Cuboid + $\frac{1}{2}$ Volume of cylinder

Find the volume of Cuboid:
Length = 10 cm
Breadth = 4 cm
Height = 6 cm

Volume of cuboid = length × breadth × height
= 10 × 4 × 6 = 240 $c{m}^3$

Find the volume of a cylinder:
Height of cylinder = 10 cm
Diameter of cylinder = Breadth of cuboid = 4 cm
$\therefore$ Radius of cylinder = 2 cm

$\text{Volume of a cylinder}=\pi r^{2}h$
$=\frac{22}{7}\left(2^2\right)\times 10cm$
$=125.71c{m}^3$

Total volume of a given solid = Volume of Cuboid + $\frac{1}{2}$ Volume of cylinder
$=240c{m}^3+\frac{125.71}{2}c{m}^3$
$=240+62.855$
$=302.855c{m}^3$