Question

Question 5: A cylindrical container has a radius of 17.5 cm and height is 18 cm. The container is filled upto 80% of its capacity with water. If water inside the container can be emptied with 30 cuboid shaped vessels whose length and breadth is 3 cm & 7 cm respectively. Find height of each cuboidal vessel. *

Answer 1

Answer:

Height of each cuboidal vessel is 22 cm.

Step-by-step explanation:

Given :

• Radius of cylindrical container is 17.5 cm.
• Height of cylindrical container is 18 cm.
• Container is filled upto 80% of its total capacity.
• Length and breadth of cuboidal vessel are 3 cm and 7 cm.

To find :

• Height of cuboidal vessel.

Solution :

We know,

• Volume of cylinder = πr²h

[Where r is radius and h is height]

Put all values :

$\longrightarrow$ Volume = 22/7 × (17.5)² × 18

$\longrightarrow$ Volume = 22/7 × 5512.5

$\longrightarrow$ Volume = 121275/7

$\longrightarrow$ Volume = 17325

Volume of cylindrical container is 17325 cm³. Means it's capacity is 17325 cm³.

• It is filled upto 80% of its capacity.

So,

$\longrightarrow$ 80% of 17325

$\longrightarrow$ 80/100 × 17325

$\longrightarrow$ 13860

80% of its capacity is 13860 cm³ means it is filled till 13860 cm³.

• If water inside the container can be emptied with 30 cuboid shaped vessels. Means 30 cuboidal vessels can be filled with 13860 cm³ of water. So,

We also know that,

• Volume of cuboid = lbh

[Where, l, b and h are length, breadth and height respectively]

$\longrightarrow$ Volume of cuboidal vessel = 3 × 7 × h

$\longrightarrow$ Volume = 21 h

And,

$\longrightarrow$ Volume of 30 cuboidal vessels = 21h × 30

$\longrightarrow$ Volume = 630h

Now,

$\longrightarrow$ Volume of 30 cuboidal vessels = 13860

$\longrightarrow$ 630h = 13860

$\longrightarrow$ h = 13860/630

$\longrightarrow$ h = 22

Thus,

Height of each cuboidal vessel is 22 cm.

Answer 2

Step-by-step explanation:

given :

• A cylindrical container has a radius of 17.5 cm and height is 18 cm. The container is filled upto 80% of its capacity with water. If water inside the container can be emptied with 30 cuboid shaped vessels whose length and breadth is 3 cm & 7 cm respectively. Find height of each cuboidal vessel.

to find :

• Find height of each cuboidal vessel. *

solution :

• Volume = 22/7 x (17.5)² x 18

• Volume = 22/7 x 5512.5

• Volume = 121275/7

• Volume =17325

• 80% of 17325

• 80/100 x 17325

• 13860

• 3 × 7 × h

• Volume = 21 h

• 21h × 30

• = 630h

• cuboidal vessels = 13860

• 630h = 13860

• h=13860/630

• h = 22

• hence, the cuboid vessels = 22cm