Question

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid is 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm, and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

Answer 1

Question:-

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid is 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm, and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

Required Answer:-

Given:-

$\\ \sf{ \rightarrow{Dimension \: of \: the \: cuboid \: pen \: stand = 10cm \: 5cm and \: 4cm}}$

$\sf{ \rightarrow{Radius \: of \: the \: conical \: depressions \: 0.5cm}}$

$\sf{ \rightarrow{Height \: of \: the \: conical \: depressions \: 2.1cm}}$

$\sf{ \rightarrow{Edge \: of \: the \: cubical \: depression \: 3cm}}$

To Find:-

$\\ \sf{ \rightarrow{Volume \: of \: the \: wood \: in \: entire \: stand}}$

♡Solution:-

First, let's find the volume of cuboid pen stand.

$\\ \underline{ \boxed{ \pmb{ \blue{Volume \: of \: cuboid = l \times b \times h}}}}$

Therefore,

$\\\sf{Volume \: of \: the \: cuboid \: pen \: stand = 10cm \times 5cm \times 4cm}$

$\sf{ \implies{Volume \: of \: the \: cuboid \: pen \: stand = (10 \times 5 \times 4) {cm}^{3} }}$

$\sf{ \implies{Volume \: of \: the \: cuboid \: pen \: stand = \bold{200{cm}^{3} }}}$

Now, the volume of conical depressions:-

$\\ \underline{ \boxed{ \pmb{ \blue{Volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h}}}}$

Therefore,

$\\\sf{Volume \: of \: conical \: depression = \frac{1}{3} \times \frac{22}{7} \times (0.5cm) {}^{2} \times 2.1cm}$

$\sf{ \implies{Volume \: of \: conical \: depression = \frac{22 \times 5 \times 5}{1000} {cm}^{3} }}$

$\sf{ \therefore{Volume \: of \: conical \: depression = \bold{0.55 {cm}^{3}}} }$

Now,

$\\\sf{Volume \: of \: 4 \: conical \: depressions = 4 \times 0.55cm {}^{3} }$

$\sf{ \therefore{Volume \: of \: 4 \: conical \: depressions= \bold{2.2 {cm}^{3}}}}$

Again, the volume of cubical depression:-

$\\ \underline{ \boxed{ \pmb{ \blue{Volume \: of \: cube = {a}^{3}}}}}$

Therefore,

$\\\sf{Volume \: of \: cubical \: depression = (3cm) {}^{3}}$

$\sf{ \therefore{Volume \: of \: cubical \: depression = \bold{ 27cm{}^{3}}}}$

Finally,

$\sf{Volume \: of \: wood} = \bold{(200 - 2.2 - 27)cm {}^{3} }$

$\sf{ \therefore{Volume \: of \: wood = \bold{ \red{170.8cm {}^{3} }}}}$

$\\ \underline{ \boxed{ \rm{ \green{Hence, \: the \: volume \: of \: wood \: in \: entire \: pen \: stand \: is \: \bold{170.8cm {}^{3} }}}}}$

Answer 2

$\huge\bf{Question:-}$

A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid is 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm, and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

$\huge\bf{Solution:-}$

(Refer to attachment)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬