Question

A rectangular container is 100 cm long and 25 cm wide. It contains 104 litres of ink when it is 50% full. Find the height of the container. Express your answer in 1 decimal place.

Answer 1

Given:-

• Length of container=100cm

• wide of container=25cm

Container contain 104 litres when it full with 50%:-

• Total quantity of ink=2×104=208 litres

Here we will change litres into two cm :-

• Volume of container=208×1000cm³

• Volume of container=208000cm³

To Find:-

• Height of the container=?

Solution:-

=> Volume of container= L × B × H

• L=100cm B=25cm H=?

=> 100 × 25 × H = 208000

=> 25 × H = 2080

=> H = 2080 / 25

=> H = 83.2 cm

• Estimated 1st decimal places:-

=> H = 83 cm

Hence,

• => The height of container= 83 cm

Answer 2

Given : Length and Breadth of Rectangular container are 100 cm & 25 cm , respectively.

Exigency To Find : The Height of the Container.

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❍ Let's Consider Height of the rectangular Container be h . [ when it is 50 % full ]

Therefore,

• The Actual Height of Container when it is 100% full will be : 2h [ when it is 100 % full ]

⠀⠀⠀⠀⠀&

• It contains l of ink when is it is half full : 104 l

Therefore,

• The half volume of Container is : 104 × 1000 = 104000 cm³ [ 1 litres = 1000 cm³ ]

$\dag\:\:\sf{ As,\:We\:know\:that\::}\\\\ \qquad\qquad \maltese\: \bf Volume \:of \: Rectangular\:Container\:[\: Cuboid\:] \: :$

$\qquad \dag\:\:\bigg\lgroup \sf{Volume_{(Cuboid)} \:: l \times b \times h }\bigg\rgroup$

⠀⠀⠀⠀⠀Here , l is the Length of Rectangular Container, b is the Breadth of Rectangular Container , h is the Height of Rectangular Container & we already know that half volume of Rectangular Container is 104000 cm³

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad:\implies \sf 104000 = 100 \times 25 \times h$

$\qquad:\implies \sf 104000 = 2500 \times h$

$\qquad:\implies \sf \dfrac{ 104000 } {2500}= h$

$\qquad:\implies \sf \cancel {\dfrac{ 104000 } {2500}}= h$

$\qquad:\implies \sf 41.6 = h$

$\qquad:\implies \bf 41.6 = h$

Therefore,

$\qquad:\implies \bf Height_{(Rectangular \:Container \:)} = \: 2 h$⠀⠀⠀

⠀⠀⠀⠀⠀⠀Here , The value of h is 41.6

$\qquad:\implies \sf Height_{(Rectangular \:Container \:)} = \: 2 h$⠀⠀

$\qquad:\implies \sf Height_{(Rectangular \:Container \:)} = \: 2 (41.6)$⠀⠀

$\qquad:\implies \bf Height_{(Rectangular \:Container \:)} = \: 83.2 \:$⠀⠀

⠀⠀⠀⠀⠀⠀Now , Estimate the value of Actual Height :

$\qquad:\implies \sf Height_{(Rectangular \:Container \:)} = \: 83.2 \approx 83 \:$⠀

$\qquad:\implies \bf Height_{(Rectangular \:Container \:)} = \: 83 \:$⠀

$\qquad :\implies \frak{\underline{\purple{\: Height_{(Rectangular \:Container \:)} = \: 83 \:cm }} }\:\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Height \:of\:Rectangular \:Container \:is\:\bf{83 \:cm }}.}}$

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