Question

A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm $\times$ 3 cm $\times$ 4 cm. Find the volume of wood in the solid object.

• A. $3918c{m}^3$
• B. $7024c{m}^3$
• C. $1444c{m}^3$
• D. $789c{m}^3$

Answer 1

The correct option is C $1444c{m}^3$

Given:
Height of the cylinder = $10\text{cm}$
Radius of the cylinder = $7\text{cm}$
Dimensions of the cuboid = $2\text{cm}\times 3\text{cm}\times 4\text{cm}$

$\text{Volume of cylinder}=V_c$
$\text{Volume of cuboidal depressions}=V_d$


$\text{Volume of the object}=V_c-4\times V_d$

Volume of cylinder, $V_c$ = $\pi r^{2}h$
$\Rightarrow V_c=\frac{22}{7}\times 7^2\times 10$
$\Rightarrow V_c=1540{\text{cm}}^3$

Volume of 4 cuboidal depressions
$=4V_d$
$=4\times l\times b\times h$
$=4\times 2\times 3\times 4$
$=96c{m}^3$

Now, volume of the solid object
$=1540-96=1444{cm}^3$

$\therefore$ Volume of wood in the solid object $=1444{cm}^3$