Question

A rectangular vessel 22 cm by 16 cm by 14 cm is full of water. If the total
water is poured into an empty cylindrical vessel of radius 8 cm, find the height
of water in the cylindrical vessel.​

Answer 1

Volume of Rectangular vessel = Volume of Cylindrical vessel { because the amount of water will be same }

Length × Breadth × Height = π R² H

=> 22 × 16 × 14 = H × 64 × π

=> π × H = 22 × 14 × 16 / 64

=> π × H = 22 × 14 / 4 { °•° 16 × 4 = 64 }

=> π × H = 22 × 7 / 2 { °•° 7 × 2 = 14 and 2 × 2 = 4 }

=> π × H = 11 × 7 { °•° 11 × 2 = 22 }

=> H = 77 / π cm or 24.5 cm

Answer 2

Answer:

The Height of the cylindrical vessel is 24.5 cm.

Step-by-step explanation:

$\textbf{\underline{\underline{Given : }}}$

Dimensions of the rectangular vessel = 22 cm × 16 cm × 14 cm

Radius of the cylindrical vessel = 8 cm

$\textbf{\underline{\underline{To find : }}}$

The height of the cylindrical vessel

$\textbf{\underline{\underline{Solution : }}}$

As the water is poured from the rectangular vessel (cuboid) to the cylindrical vessel, the volume of both would be same.

✯ $\textsf{\underline{\underline{Volume of the cuboid - }}}$

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

$\sf{\longrightarrow} \: 22 \times 16 \times 14 \\ \\ \sf{\longrightarrow} \: 4928 \: {cm}^{3}$

Volume of the cuboid = 4928 cm³

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Height of the cylindrical vessel -}}}$

Let the height be h

The Volume of Cuboid and the cylindrical vessel is same.

$\boxed{\sf{Volume \: of \:cylinder = \pi r^{2} h}}$

$\sf{\longrightarrow} \: \dfrac{22}{7} \times 8 \times 8 \times h = 4928 \\ \\ \sf{\longrightarrow} \: \dfrac{22 \times 64h}{7} = 4928 \\ \\ \sf{\longrightarrow} \: \dfrac{1408h}{7} = 4928 \\ \\ \sf{\longrightarrow} \: 1408h = 4928 \times 7 \\ \\ \sf{\longrightarrow} \: 1408h = 34496 \\ \\ \sf{\longrightarrow} \: h = \dfrac{34496}{1408} \\ \\ \sf{\longrightarrow} \: h = 24.5$

Height = 24.5 cm

$\therefore$ The Height of the cylindrical vessel is 24.5 cm.