Question

A rectangular vessel of dimensions 20cm by15cm by 11cm is full of water. If the water is poured into an empty cylindrical vessel of radius10 cm, find the height of water in the cylindrical vessel.

Answer 1

Given :-

Dimensions of the rectangular vessel :-

• Length = 20cm

• Breadth = 15cm

• Height = 11cm

ATQ,

The water in the rectangular vessel is poured into an empty cylindrical vessel of radius 10cm.

Here, we've to find the height of water in the cylindrical vessel.

So first of all, we needa find the volume of the rectangular vessel in order to find the total amount of water.

Volume of the rectangular vessel (cuboid) = length × breadth × height

= 20 × 15 × 11

= 3300cm³

Thus the volume of of water in the cylindrical vessel is also = 3300cm³

We know that,

πr²h = volume of a cylinder

➡ 22/7 × 10 × 10 × h = 3300cm³

➡ 2200/7 × h = 3300cm³

➡ h = 3300/1 × 7/2200

➡ h = 1.5 × 7

➡ h = 10.5cm

Hence, the height of water present in the cylindrical vessel is 10.5cm.

Answer 2

Answer :

The height of water present in the cylindrical vessel is 10.5cm.

Step-by-step explanation :

Given that :

• Breadth = 15 cm.
• Length = 20 cm.
• Height = 11 cm.

To Find :

The height of water in the cylindrical vessel.

Solution :

The First step is to Find the Volume the rectangular vessel. Because, it will help us to find the total amount of water.

We know that :

$\bigstar\;\boxed{\sf Volume = Length \times Breadth \times Height}}$

Put the given values :

$\sf \implies 20 \times 15 \times 11$

$\sf \implies 3300cm^3$

$\therefore$ Volume of of water in the cylindrical vessel is = $\sf 3300cm^3$

We also know :

$\bigstar\;\boxed{\sf Volume\;of\;a\;Cylinder = \pi r^2h}}$

Plug the values :

$\sf \implies 3300cm^3 = \dfrac{22}{7}\times 10 \times 10 \times H$

$\sf \implies 3300cm^3 = \dfrac{2200}{7} \times H$

$\sf \implies H = \dfrac{3300}{1} \times \dfrac{7}{2200}$

$\sf \implies H = 7 \times 1.5$

$\sf \implies H = 10.5cm.$

$\bigstar\;\textbf{\underline{\underline{Hence,The height of water present in the cylindrical vessel is 10.5cm.}}}$