Question

A cuboid vessel is 10 cm long and 8 cm wide. how high must it be made to hold for 480 cubic centimetres of a liquid ?​

Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• A cuboid vessel is 10 cm long and 8 cm wide. how high must it be made to hold for 480 cubic centimetres of a liquid ?

$\large\underline{ \underline{ \sf \maltese{ \: Given:- }}}$

• Volume of the Cuboidal Vessel = $\sf\green{ 480{cm}^{3}}$
• Length of the Cuboidal Vessel = $\sf\green{ 10cm}$
• Breadth of the Cuboidal Vessel = $\sf\green{ 8cm}$

$\large\underline{ \underline{ \sf \maltese{ \: To \: Find :- }}}$

• Height of the Cuboidal Vessel ?

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: Volume \: = \: Length \: \times \: Breath \: \times \: Height }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\qquad \quad {:} \longrightarrow \bf{\bf{Height \: = \: \frac{Volume}{Length \: \times \: Breadth} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Height \: of \: the \: Cuboidal \: Vessel \: =\: \frac{480}{10 \: \times \: 8} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Height \: of \: the \: Cuboidal \: Vessel \: =\: \frac{48\cancel0}{1\cancel0 \: \times \: 8} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Height \: of \: the \: Cuboidal \: Vessel \: =\: \frac{48}{ 8} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{Height \: of \: the \: Cuboidal \: Vessel \: =\: \cancel\frac{48}{ 8} }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{Height \: = \:6 cm }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ \: Height \: of \: the \: Cuboidal \: Vessel\: = \underline {\underline{ 6cm}}}\\\end{gathered}\end{gathered}$

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$\underbrace\red{\boxed{ \sf \blue{ Diagram\: of \: Cuboidal \: Vessel }}}$

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf 10\:cm}\put(7.7,6.3){\sf 8\:cm}\put(11.3,7.45){\sf 6\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

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More For Knowledge:-

$\underbrace\orange{\boxed{ \sf \green{ Standard\: Units \:of \: Volumes}}}$

$\qquad \quad {:} \longrightarrow \bf{\bf{ 1{m}^{3} \: = \: 1000000 {cm}^{3} }}$

$\qquad \quad {:} \longrightarrow \bf{\bf{ 1{m}^{3} \: = \: 1000{dm}^{3} \: = \: 1000 \: litres }}$

$\qquad \quad {:} \longrightarrow \bf{\bf{ 1{dm}^{3} \: = \: 1000{cm}^{3} \: = \: 1000 \: mililitres }}$

$\qquad \quad {:} \longrightarrow \bf{\bf{ 1kilo \: litre \: = \: 1000 \: litre \: = \: {10}^{6} \: {cm}^{3} \: = \: 1 {m}^{3} }}$

$\qquad \quad {:} \longrightarrow \bf{\bf{ 1 \: {cm}^{2} \: = \: 1000 {mm}^{3} }}$

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Answer 2

Answer:

volume of cuboid = volume of liquid

length × width × height =480 m

3

10×8× height =480

⇒ height of cuboid require =

8×10

480

=6m