Question

If 70% of the volume from a 10 cm cubical container is poured into a cuboidal vessel of length 20 cm, breadth 15 cm and height 10cm, what fraction of the cuboidal vessel is occupied ?

Answer 1

$\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cubical}\mathrm{vessel}={\left(10\mathrm{cm}\right)}^3=1000{\mathrm{cm}}^3=1000\mathrm{ml}\mathrm{Volume}\mathrm{poured}\mathrm{to}\mathrm{the}\mathrm{cuboidal}\mathrm{vessel}=70\%\mathrm{of}1000\mathrm{ml}=700\mathrm{ml}\mathrm{Length}\mathrm{and}\mathrm{breadth}\mathrm{of}\mathrm{cuboidal}\mathrm{vessel}=20\mathrm{cm}\mathrm{and}15\mathrm{cm}\mathrm{respectively}\mathrm{Base}\mathrm{area}=\mathrm{Length}\times \mathrm{Breadth}=(20\times 15){\mathrm{cm}}^2=300{\mathrm{cm}}^2\mathrm{Volume}\mathrm{in}\mathrm{the}\mathrm{vessel}=700\mathrm{ml}=700{\mathrm{cm}}^3\mathrm{Height}\mathrm{in}\mathrm{the}\mathrm{cuboidal}\mathrm{vessel}=\frac{\mathrm{Volume}}{\mathrm{Base}\mathrm{area}}=\frac{700}{300}\mathrm{cm}=\frac{7}{3}\mathrm{cm}\mathrm{Total}\mathrm{height}\mathrm{of}\mathrm{the}\mathrm{vessel}=10\mathrm{cm}\mathrm{Fraction}\mathrm{of}\mathrm{vessel}\mathrm{occupied}=\frac{\mathrm{Height}\mathrm{filled}}{\mathrm{Total}\mathrm{height}}=\frac{7}{3\times 10}=\frac{7}{30}$