Question

Find the difference of the volume of the two tanks of the following dimensions, in and liters. Tank-1, $ l = 35{\text{ cm}} $ , $ b = 20{\text{ cm}} $ and $ h = 20{\text{ cm}} $ . Tank-2, $ l = 40{\text{ cm}} $ , $ b = 24{\text{ cm}} $ and $ h = 24{\text{ cm}} $

Answer 1

Hint: The volume of cuboidal tank-1 and tank-2 is calculated using $ V = lbh $ . After calculating the volume their difference is calculated .The units are given in centimeters, the units of volume will be in cubic centimeters. To convert the volumes in liter multiply the volume in cubic centimeters by a factor $ \dfrac{1}{{1000}} $ as $ 1{\text{ L = 1000 c}}{{\text{m}}^3} $ .

Complete step-by-step answer:
The given information about the dimensions of the two tanks, tank-1 and tank-2 are as follows
Tank-1
Length of the tank-1, $ {l_1} = 35{\text{ cm}} $
Breadth of the tank-1, $ {b_1} = 20{\text{ cm}} $
Height of the tank-1, $ {h_1} = 20{\text{ cm}} $
Tank-2
Length of the tank-2, $ {l_2} = 40{\text{ cm}} $
Breadth of the tank-2, $ {b_2} = 24{\text{ cm}} $
Height of the tank-2, $ {h_2} = 24{\text{ cm}} $
Volume of tank-1 is calculated using the following expression,
 $ \Rightarrow {V_1} = {l_1} \times {b_1} \times {h_1} \cdots \left( 1 \right) $
Substitute the value of $ {l_1} = 35{\text{ cm}} $ , $ {b_1} = 20{\text{ cm}} $ and $ {h_1} = 20{\text{ cm}} $ in equation (1), we get
 $ \Rightarrow {V_1} = 35{\text{ cm}} \times 20{\text{ cm}} \times 20{\text{ cm}} $
 $ \Rightarrow {V_1} = 14000{\text{ c}}{{\text{m}}^3} \cdots \left( 2 \right) $
To convert the volume in liter multiply the volume in cubic cm. by a factor of $ \dfrac{1}{{1000}} $
 $ {V_1} = 14000 \times \dfrac{1}{{1000}}{\text{ L}} $
 $ \Rightarrow {V_1} = 14{\text{ L}} \cdots \left( 3 \right) $
Volume of tank-2 is calculated using the expression as follows,
 $ \Rightarrow {V_2} = {l_2} \times {b_2} \times {h_2} \cdots \left( 4 \right) $
Substitute the value of $ {l_2} = 40{\text{ cm}} $ , $ {b_2} = 24{\text{ cm}} $ and $ {h_3} = 24{\text{ cm}} $ in equation (4) we get
 $ \Rightarrow {V_2} = 40{\text{ cm}} \times {\text{24 cm}} \times 24{\text{ cm}} $
 $ \Rightarrow {V_2} = 23040{\text{ c}}{{\text{m}}^3} \cdots \left( 5 \right) $
To convert the volume in liters multiply by the volume in cubic cm. by $ \dfrac{1}{{1000}} $
 $ \Rightarrow {V_2} = 23040 \times \dfrac{1}{{1000}}{\text{ L}} $
 $ \Rightarrow {V_2} = 23.04{\text{ L}} \cdots \left( 6 \right) $
Difference of the volume of the two tanks in cubic cm. is
 $ \Rightarrow V = {V_2}({\text{c}}{{\text{m}}^3}) - {V_1}({\text{c}}{{\text{m}}^3}) \cdots \left( 7 \right) $
Substitute the value of $ {V_1} = 14000{\text{ c}}{{\text{m}}^3} $ and $ {V_2} = 23040{\text{ c}}{{\text{m}}^3} $ in equation (7) we get
 $
\Rightarrow V = 23040 - 14000 \\
\Rightarrow V = 9040{\text{ c}}{{\text{m}}^3} \;
  $
Difference of the volume of the two tanks in Liters is,
 $ V = {V_2}({\text{Litres}}) - {V_1}({\text{Litres}}) \cdots \left( 8 \right) $
Substitute the value of $ {V_1} = 14{\text{ L}} $ and $ {V_2} = 23.04{\text{ L}} $ in equation (8)
 $
\Rightarrow V = 23.04 - 14 \\
\Rightarrow V = 9.04{\text{ L}} \;
  $
Hence, the difference of the volume of the tank in cubic cm. is $ 9040{\text{ c}}{{\text{m}}^3} $ and in liters is $ 9.04{\text{ L}} $ .

Note: The important step is to remember the conversion factor from cubic cm. to liters is $ \dfrac{1}{{1000}} $ as $ 1000{\text{ c}}{{\text{m}}^3} = 1{\text{ L}} $ .
The capacity of the tank is expressed in various units based on the convenience. Some of the important units are cubic meter, cubic centime, liters, gallons, etc.