Question

Two cylindrical vessels are with filled with oil. Their radii are 15cm, 12cm and the height 20cm, 16cm respectively. Find the radius of cylindrical vessel 21cm in height. which will just contain the oil of the two given vessels

Answer 1

Answer:

Radius of the cylindrical vessel which contain oil of  the both vessels is 18 cm  

Step-by-step explanation:

SOLUTION :  

Given :  

Radius of the first cylindrical vessel ,R = 15 cm

Height of the first cylindrical vessel ,H = 20 cm

Radius of the second cylindrical vessel , r = 12 cm

Height of the second cylindrical vessel ,h  = 16 cm

Height of the cylindrical vessel which contain oil of the given two vessels (H1) = 21 cm.

Volume of the first cylindrical vessel = πR²H

= π × 15 × 15 × 20 = 4500 π

Volume of the first  cylindrical vessel  = 4500π cm³

Volume of the second cylindrical vessel = πr²h

= π × 12 × 12 × 16 = 1304 π  

Volume of the second cylindrical vessel = 1304 π cm³

Let r1 be the Radius of the cylindrical vessel which contain oil of  the both vessels

Volume of the cylindrical vessel which contain oil of  the both vessels = Volume of the first vessel + Volume of the second vessel.

πr1²H1 = 4500 π + 1304 π  

πr1² ×21= π(4500 + 1304)

r1² ×21= 6804

r1² = 6804/21

r1² = 324

r1 = √324

r1 = 18 cm  

Hence, the radius of the cylindrical vessel which contain oil of  the both vessels is 18 cm  

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer:

${\bold{\red{\huge{Your\:Solution}}}}$

Step-by-step explanation:

The Volume of 1st cylindrical vessel

=> \pi X (15)^{2} X 20\\\\

=> 225 X 20 X \pi \\\\

=> 4500\pi cm^{2}[/tex]

The Volume of 2nd cylindrical vessel

$=> \pi X (12)^{2}  X  16\\</p><p></p><p>=> 144  X  16   X   \pi \\</p><p></p><p>=> 1305\pi cm ^{2}$

Let r be the radius of the vessel ,which will just contain oil of the both vessels

Therefore,

Volume of Cylinder Vessel = Sum of the Volume of both Vessels

i.e,

$\pi r^{2} h=4500\pi +2304\pi$

$\pi ^{2}  X  21 => 6804\pi$ ( $(both\pi cuts)$

$\pi ^{2} = \frac{6804}{21}$

$r^{2} = 324$

$r^{2} = 18$

${\bold{\orange{\huge{Hope\:it\:Helps}}}}$