Question

5. Two cylindrical vessels are filled with water.
The radius of one vessel is 15 cm and its height
is 25 cm. The radius and height of other vessel
are 10 cm and 18 cm respectively. Find the
radius of cylindrical vessel of height 30 cm
which can just contain the water of the two
given vessels.​

Answer 1

$\huge{\underline{\underline{\sf{\red{Required\:Solution:}}}}}$

For one vessel

⠀⠀⠀⠀⠀⠀⠀Rαdius (R) = 15 cm

⠀⠀⠀⠀⠀⠀⠀Height (H) = 25 cm

${\therefore}$⠀⠀⠀⠀⠀Volume$\displaystyle{\sf{(v_1)= \pi R^{2}H}}$

⠀⠀⠀⠀⠀⠀⠀$\displaystyle{\sf{= \pi (15)^{2}(25)}}$

⠀⠀⠀⠀⠀⠀⠀:$\implies{\boxed{\sf{\orange{= 5625 \pi cm^{3}}}}}$

For other vessel

⠀⠀⠀⠀⠀⠀⠀Rαdius (r) = 10 cm

⠀⠀⠀⠀⠀⠀⠀Height (h) = 18 cm

${\therefore}$⠀⠀⠀⠀⠀Volume$\displaystyle{\sf{(v_2)= \pi r^{2}h}}$

⠀⠀⠀⠀⠀⠀⠀$\displaystyle{\sf{= \pi (10)^{2}(18)}}$

⠀⠀⠀⠀⠀⠀⠀$\displaystyle{\sf{= 1800 \pi cm^{3}}}$

Let the radius of the third cylinderical vessel be x cm.

⠀⠀⠀⠀⠀⠀⠀$\displaystyle{\sf{Height(h^{1})=30cm}}$

${\therefore}$⠀⠀⠀⠀⠀$\displaystyle{\sf{Volume(v_3)= \pi x^{2} h^{1}}}$

⠀⠀⠀⠀⠀⠀⠀$\displaystyle{\sf{= \pi x^{2}\:(30)}}$

⠀⠀⠀⠀⠀⠀⠀:$\implies{\boxed{\sf{\pink{ 30 \pi x^{2}\:cm^{3}}}}}$

According to the question,

$\displaystyle{\sf{v_3 = v_1 + v_2}}$

$\implies{\sf{30 \pi x^{2} = 5625\pi + 1800\pi}}$

$\implies{\sf{30x^{2} = 7425}}$

$\implies{\sf{x^{2} = \dfrac{7425}{30}}}$

$\implies{\sf{x^{2} = \dfrac{495}{2}}}$

$\implies{\sf{x = \sqrt{ \dfrac{495}{2}}}}$

• Hence the required height is $\displaystyle{\sf{ \sqrt{ \dfrac{495}{2}}cm}}$

__________________________

Answer 2

Step-by-step explanation:

Two cylindrical vessels are filled with water.

The radius of one vessel is 15 cm and its height

is 25 cm. The radius and height of other vessel

are 10 cm and 18 cm respectively. Find the

radius of cylindrical vessel of height 30 cm

which can just contain the water of the two

given vessels.