Question

A cube of 9cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15cm and 12cm.Find the rise of water in the vessel. ​

Answer 1

${\red{\underline{\underline{\bold{Given:-}}}}}$

• Edge of cube = 9cm
• Dimensions of the base of rectangular vessel = 15cm and 12cm

${\blue{\underline{\underline{\bold{To\:Find:-}}}}}$

• The rise of water in the rectangular vessel

${\green{\underline{\underline{\bold{Solution:-}}}}}$

We have,

Edge of cube = 9cm

Volume of cube = ${9}^{3} = 729{cm}^{3}$

If the cube is immersed in the vessel, then the water level rises

Let the rise in the water level be x cm

Clearly,

Volume of cube = Volume of water replaced by it

Volume of cube = Volume of cuboid of dimensions - 15cm×12cm× x cm

$\implies 729 = 15×12×x \\ \\</p><p></p><p>\implies x = \frac {729}{15×12} \\ \\</p><p></p><p>\implies x = \frac{81}{20} = 4.05 cm$

______________

Formulas used:-

• Volume of cube = ${Edge}^{3} = {Side}^{3}$
• Volume of cuboid = length × breadth × height

_______________

Additional Information:-

• Volume of cylinder = π${r}^{2}$h
• Volume of hollow cylinder = Exterior volume- Interior volume = π${R}^{2}$h - π${r}^{2}$h = π(${R}^{2}-{r}^{2}$)h
• Volume of cone = $\frac{1}{3} π {r}^{2}h$

Answer 2

Step-by-step explanation:

Given:−

Edge of cube = 9cm

Dimensions of the base of rectangular vessel = 15cm and 12cm

{\blue{\underline{\underline{\bold{To\:Find:-}}}}}

ToFind:−

The rise of water in the rectangular vessel

{\green{\underline{\underline{\bold{Solution:-}}}}}

Solution:−

We have,

Edge of cube = 9cm

Volume of cube = {9}^{3} = 729{cm}^{3}9

3

=729cm

3

If the cube is immersed in the vessel, then the water level rises

Let the rise in the water level be x cm

Clearly,

Volume of cube = Volume of water replaced by it

Volume of cube = Volume of cuboid of dimensions - 15cm×12cm× x cm

\begin{lgathered}\implies 729 = 15×12×x \\ \\ \implies x = \frac {729}{15×12} \\ \\ \implies x = \frac{81}{20} = 4.05 cm\end{lgathered}

⟹729=15×12×x

⟹x=

15×12

729

⟹x=

20

81

=4.05cm

______________

Formulas used:-

Volume of cube = {Edge}^{3} = {Side}^{3}Edge

3

=Side

3

Volume of cuboid = length × breadth × height

_______________

Additional Information:-

Volume of cylinder = π{r}^{2}r

2

h

Volume of hollow cylinder = Exterior volume- Interior volume = π{R}^{2}R

2

h - π{r}^{2}r

2

h = π({R}^{2}-{r}^{2}R

2

−r

2

)h

Volume of cone = \frac{1}{3} π {r}^{2}h

3

1

πr

2

h