Question

The diameter of a cylindrical bucket is 28
cm and it contains water to a height of
64 cm. This water is emptied into a rectan-
gular tank 88 cm long and 28 cm wide. The
height of water level in the tank is :
(a) 44 cm (b) 22 cm (c) 14 cm (d) 16 cm​

Answer 1

Given :-

• The diameter of a cylindrical bucket is 28cm and it contains water to a height of 64 cm.  

• This water is emptied into a rectangular tank 88 cm long and 28 cm wide.  

To Find :-

• The height of water level in the tank is ?

Solution :-

~Here, we’re given the dimensions of a cylindrical bucket and it contains water in it . Then the water is emptied into a rectangular tank whose length and width is given to us. The volume of cylindrical bucket is equal to the rectangular tank’s volume. Firstly , we’ll find the radius as we’re given the diameter, then volume of cylindrical tank and then height of the rectangular tank by putting the values in the formula of finding it’s volume .

____________

As we know that ,

$\boxed{\bf{ \maltese \;\; Radius = \dfrac{Diameter}{2} }}$

$\boxed{\bf{ \maltese \;\; Volume\;of\;cylinder = \pi r^{2} h }}$

Where,  

• r is radius  
• h is height

$\boxed{\bf{ \maltese \;\; Volume\;of\;cuboid = lbh }}$

Where,  

• l is length  

• b is breadth  

• h is height  

_____________

Finding the radius ::  

$\sf \implies \dfrac{28}{2}$

$\boxed{\sf{ \star \;\; Radius = \;\; 14\;cm }}$

Finding the volume of cylindrical bucket ::

$\sf \implies \dfrac{22}{7} \times 14 \times 14 \times 64$

$\sf \implies 22 \times 2 \times 14 \times 64$

$\boxed{\sf{ \star \;\; Volume = 39,424 \;cm^{3} }}$

Finding the height of rectangular tank ::

$\sf \implies 88 \times 28 \times h = 39,424$

$\sf \implies 2464 \times h = 39424$

$\boxed{\sf{ \star \;\; height = 16\;cm }}$  

__________

Hence,  

• Height of the rectangular tank is 16 cm

        ( Option d )  

__________

Answer 2

Question ⤵

The diameter of a cylindrical bucket is 28 cm and it contains water to a height of 64 cm. This water is emptied into a rectan- gular tank 88cm long and 28 cm wide. The height of water level in the tank is :

(a) 44 cm (b) 22 cm (c) 14 cm (d) 16 cm

___________________________________

Solution ⤵

Volume of Cuboid ☞ L×B×H

Finding the radius :: $\sf \implies \dfrac{28}{2}$

$\boxed{\sf{ \; Radius = \;\; 14\;cm }}$

___________________________________

Finding the volume of cylindrical bucket :

$\sf \implies \dfrac{22}{7} \times 14 \times 14 \times 64$

$\boxed{\sf{ \; Volume = 39,424 \;cm^{3} }}$

___________________________________

Finding the height of rectangular tank ::

$\sf \implies 88 \times 28 \times h \\ = 39,424$

$\sf \implies 2464 \times h = 39424</p><p>⟹2464×h =39424$

$\boxed{ \; height = 16\;cm}$

___________________________________

Correct Option is (d) 16 cm