Answer:
[tex]\large\boxed{\pink{\sf \leadsto The \ Volume \ of \ water \ needed \ to \ be \ filled \ is \ 192,500 cm^3}}[/tex]
Step-by-step explanation:
Given that , cylindrical vessel is 70 cm high and the radius of its base is 35cm . it contains some water up to the height of 20 cm .
And we need to find the water required to fill it completely .
Figure :-
[tex]\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\linethickness{0.4mm}\put(0,0){\line(0,1){5}} \put(3,0){\line(0,1){5}}\qbezier(0,5)(1.5,4)(3,5)\qbezier(0.001,0)(1.5,1)(3,0)\qbezier(0,5)(1.5,6)(3,5)\qbezier(0.001,0)( 1.5, - 1)(3,0)\put(3.5,2){\vector(0,-1){2}}\put(3.5,3){\vector(0,1){2}}\put(3.5,2.5){$\sf 70 cm $}\put(1.4,0){\line(1,0){1.6}} \put(1.4,0.2){$\sf 35cm$}\qbezier(0,2.5)(1.5,3.5)(3,2.5)\qbezier(0,2.5)(1.5, 1.8)(3,2.5)\put(-1,1){\vector(0,-1){1}}\put(-1,1.5){\vector(0,1){1}}\put(-1.3,1.2){$\sf 20cm $}\end{picture}[/tex]
Let us take the Volume of Cylinder be V and the volume of cylinder filled be v . Let the volume required to be filled be X .
From the figure it's clear that , Volume of water required to fill the cylindrical vessel completely will be :-
[tex]\tt:\implies v + x = V \:\: \bigg\lgroup \red{\bf As \ per \ our \ assumption }\bigg\rgroup \\\\\tt:\implies x = V - v \\\\\tt:\implies x = \pi r^2 H - \pi r^2 h \\\\\tt:\implies x = \pi r^2 ( H - h ) \\\\\tt:\implies x = \pi r^2 ( 70 cm - 20 cm ) \\\\\tt:\implies x = \dfrac{22}{7} \times (35 cm)^2 \times 50 cm \\\\\tt:\implies x = \dfrac{22\times 35 cm \times 35 cm }{7} \times 50 cm \\\\\underline{\boxed{\red{\tt \longmapsto Volume_{fill } = 192,500 cm^3}}}[/tex]
Hence the required volume of water to be filled is 192,500 cm³.
