A cylindrical vessel having diameter equal to its height is full of water which is poured into two identical cylindrical vessels with diameter 42 cm and height 21 cm which are filled completely. Find the diameter of the cylindrical vessel.
Answers
Answer:
The diameter of cylindrical vessel is 42 cm.
Step-by-step explanation:
Given :
Diameter of identical cylindrical vessel , d = 42 cm
Height of identical cylindrical vessel , h = 21 cm
Diameter of cylindrical vessel is equal to height of a cylindrical vessel
Height of cylindrical vessel = Diameter of cylindrical vessel
h = d
h = 2r …………(1)
[ Diameter = 2 × Radius]
Radius of identical cylindrical vessel = 42/2 = 21 cm
Volume of cylindrical vessel = πr²h
= πr²(2r) = 2πr³
[From eq 1]
Volume of cylindrical vessel becomes = 2πr³
Volume of each identical vessel = πr²h
Since volumes are equal , then
Volume of cylindrical vessel = Volume of two identical cylindrical vessels
2πr³ = 2 ×( πr²h)
r³ = r² × 21
r³/r² = 21
r = 21
Radius of cylindrical vessel , r = 21cm
Diameter of cylindrical vessel = 2r = 2 × 21 = 42cm.
Hence, the diameter of cylindrical vessel is 42 cm.
HOPE THIS ANSWER WILL HELP YOU...
Answer:Hi ,
1 ) dimensions of the large cylider
diameter = d cm
Height = h = d cm
Volume = π( d/2)² h
= π ( d ²/ 4)×d
= π d³/4 ----( 1 )
2 ) dimensions of the smaller cylider
d = 42 cm
h = 21 cm
Volume = π × ( d²/ 4 ) × h
= ( π × 42 × 42 × 21 )/4---( 2 )
According to the problem given ,
( 1 ) = 2 × ( 2 )
π d³/4 = 2 × ( π × 42 × 42 × 21 )/4
d³ = ( 2 π × 42 × 42 × 21 × 4 )/(π×4)
d³ = ( 42 )³
Therefore ,
d = 42 cm
I hope this helps you.
:)