Question

A village having population of 400, requires 150 l

Of water per head per day. It has a tank measuring

20m×15m×6m.

a. Find the volume of water used by the village people per day.

b. Find the volume of the tank.

c. 1 m³ = ________l

d. How many days will the water of this tank last?

e. Find the total Surface area of the tank.​

Answer 1

$\LARGE\mathfrak{\underline{\underline\textcolor{violet}{✪\: \: \: Given :-}}}$

$\large\texttt{↦ Population of the village = 400}\\\\\large\texttt{↦ Water used by a person each day = 150 L }\\\\\large\texttt{Dimensions of the tank = 20m × 15m × 6m .}$

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$\LARGE\mathfrak{\underline{\underline\textcolor{violet}{✪\: \: \: To\: \: Find :-}}}$

❶ Volume of the water used by the village per day = ?

❷ Volume of the tank = ?

❸ 1 m³ = _____ L

❹ Number of days the water in the tank will last = ?

❺ Total surface area of the tank = ?

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$\LARGE\mathfrak{\underline{\underline\textcolor{violet}{✪\: \: \: Formula :-}}}$

$\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{red}{ T.S.A. _ { ( \: Cuboid \: ) } = 2 ( LB + BH + HL ) }}}\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf\textcolor{red}{ Volume_{ ( \: Cuboid \: ) } = L × B × H }}}$

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$\LARGE\mathfrak{\underline{\underline\textcolor{violet}{✪\: \: \: Answer :-}}}$

❶ Volume of the water used by the village per day :-

• To find this we have to multiple the Amount of the water used by a single person × Total number of the person's in the whole village .

$\large: \: \Longrightarrow\textsf{150 × 400}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\mathfrak\textcolor{magenta}{= 60000 \: L}}}$

• Volume of the water used by the whole village per day = 60,000 L .

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❷ Volume of the tank :-

• As we know that the tank is in a Cuboidal Shape so we have to use the Formula of the ' Volume of a cuboid ' .

$\large\: \bigstar\textsf\textcolor{orange}{\: \: \: Volume_{ ( \: Cuboid \: ) } = L × B × H }\\\\\\\large: \: \Longrightarrow\textsf{= 20 × 15 × 6 }\\\\\\\large : \: \Longrightarrow\underline{\boxed{\mathfrak\textcolor{magenta}{= 1800\: m³}}}$

• So , the volume of the tank = 1800 m³ .

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❸ 1m³ = 1000 L .

➛ 1800 m³ = 18,00,000 L

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❹ Number of days the water in the tank will last :-

• We have to calculate this by the Total Volume of the tank ÷ Total Volume the water required for the whole village per day .

• Volume of the tank = 18,00,000 L

• Per day requirement of the water for the village = 60,000 L .

$\large: \: \Longrightarrow\textsf{= \cfrac{ 1800000}{60000} }\\\\\\\large: \: \Longrightarrow\textsf{= \cancel\cfrac{1800000}{60000} }\\\\\\\large : \: \Longrightarrow\underline{\boxed{\mathfrak\textcolor{magenta}{= 30 \: Day's}}}$

• So the water in the tank will last for 30 Days .

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❺ Total Surface Area of the tank :-

• As we know that the tank is in the Cuboidal Shape so we have to use the Formula of T.S.A. of a cuboid .

$\large\: \bigstar\textsf\textcolor{orange}{\: \: \: T.S.A. _ { ( \: Cuboid \: ) } = 2 ( LB + BH + HL ) }\large: \: \Longrightarrow\textsf{= 20 × 15 + 15 × 6 + 20 × 6}\\\\\\\large: \: \Longrightarrow\textsf{= 2 ( 300 + 90 + 120 ) }\\\\\\\large : \: \Longrightarrow\underline{\boxed{\textsf{= 2 × 516 }}}\\\\\\\large : \: \Longrightarrow\underline{\boxed{\mathfrak\textcolor{magenta}{= 1032 \: m²}}}$

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