Question

3080cm3 of water is required to fill a cylindrical vessel completely and 2310cm3 of water is required to fill it upto 5cm below the top. Find radius and height of vessel

Answer 1

hello users ......

we have given that:-
3080cm3 of water is required to fill a cylindrical vessel completely and 2310cm3 of water is required to fill it upto 5cm below the top

we have to find :-
height and radius of cylinder

solution:-
we know that :
volume of cylinder = πr²h
where
r is radius and h is the height of cylinder


here,
let height of cylinder = h cm
and
radius = r cm

here ,
according to question
πr²h = 3080 cm³ (volume of cylinder)

now ,
the height of cylinder up to 5 cm below the top = (h-5)

again ,
according to question
πr²(h-5) = 2310 cm³
(volume of cylinder up to 5 cm from top )
= πr²h -5πr² = 2310 cm³
=> -5πr² = 2310 - πr²h

=> -5πr² = 2310 -3080 = -770

=> πr² = 770/5 = 154

=> r² = 154× 7 / 22

=> r² = 49

=> r= 7 cm

now ,
again
πr²h = 3080
here
hπ = 3080 /49 = 62.85

=> h = 62.85 / 3.14 = 20 .01 cm

=> h = 20cm approximate

hence ,
radius = 7 cm & height =20 cm

⭐⭐ hope it helps ⭐⭐

Answer 2

Question:

15. 3080 cm³ of water is required to fill a cylindrical vessel completely and 2310 cm³ of water is required to fill it upto 5 cm below the top. Find:

(i) radius of the vessel.

(ii) height of the vessel.

(iii) wetted surface area of the vessel when it is half-filled with water.

* Solution * . Volume of water to fill a cylindrical vessel= 3080 cm³

Volume of water to fill it upto 5 cm below= 2310 cm²

.. Volume of water for 5 cm height = 3080-2310= 770 cm³

(1) Let r be the radius of vessel then

(pie) r²h=770 => 22/7 x r² x5 = 770

r => 770x7 / 22x5 =49=(7)²

r=7cm

Height of vessel = 3080 / 770 x 5= 20 cm

Area of half wetted cylinder ,

1/ 2 × 2 (pie) r h + (pie) r²

= pie] (h+r)

22 / 7 × 7(20+7)

=22x27=594 cm²