Question

A cylindrical jar has juice, the diameter of
cylindrical jar is 30 cm and height 32 cm. How
many cylindrical glasses can be filled by this
juice, if diameter of each glass is 6 cm and height
8 cm.​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• A cylindrical jar has juice, the diameter of cylindrical jar is 30 cm and height 32 cm

• Diameter and height of cylindrical glasses are 6 cm & 8 cm respectively

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• The number of cylindrical glasses that can be filled by juice in cylindrical jar

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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$\boxed { \rm Radius = \dfrac { Diameter } { 2 } }$

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$\rm Radius _{\bf \red{ \: jar } } = \dfrac { 30 } { 2 }$

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• $\sf Radius _{\bf \red{ \: jar }} = 15 \: cm$

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$\rm Radius _{\bf\green{ \: glass} } = \dfrac { 6 } { 2 }$

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• $\sf Radius _{\bf \green { \: glass } } = 3 \: cm$

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We will calculate the volume of cylindrical jar to get the amount of juice the cylindrical jar contains

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$\underline{\bold{\texttt{Volume of cylinder :}}}$

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➠ πr²h ⚊⚊⚊⚊ ⓵

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Where ,

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• r = Radius

• h = Height

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$\underline{\bold{\texttt{Volume of cylindrical jar :}}}$

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• r = 15 cm

• h = 32 cm

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⟮ Putting the above values in ⓵ ⟯

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➜ πr²h

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➜ $\sf \pi \times 15 \times 15 \times 32$ ⚊⚊⚊⚊ ⓶

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• $\sf Total \: Juice = \pi \times 15 \times 15 \times 32 \: cu. \: cm.$

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Now let's calculate the amount of juice a cylindrical glass can store

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$\underline{\bold{\texttt{Volume of cylindrical glass :}}}$

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• r = 3 cm

• h = 8 cm

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⟮ Putting the above values in ⓵ ⟯

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➜ πr²h

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➜ $\sf \pi \times 3 \times 3 \times 8$ ⚊⚊⚊⚊ ⓷

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• $\sf Total \: juice \: 1 \: glass \: can \: store = \pi \times 3 \times 3 \times 8 \: cu. \: cm.$

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We will divide Total amount of juice by the total amount of juice each glass can store to find the numbers of cylindrical glasses that can be filled by juice in cylindrical jar

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Thus ,

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Equation ⓶ ÷ Equation ⓷

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➜ $\sf \dfrac { \pi \times 15 \times 15 \times 32 } { \pi \times 3 \times 3 \times 8 }$

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➜ $\sf 5 \times 5 \times 4$

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➜ $\sf 5 \times 20$

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➨ $\sf 100$

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• Hence 100 cylindrical glasses can be filled by the juice in cylindrical jar

Answer 2

Given -

• Diameter of Jar is 30cm
• Height of Jar is 32 cm

• Diameter of each glass is 6cm
• Height of each glass is 8cm

To find -

• Number of glasses, that can be filled by juice.

Formula used -

• Volume of cylinder.

Solution -

In the question,new are given with the diameter and height of a Cylindrical Jar, and Diameter and height of glasses, and we need to find the number of glasses, that can be filled with juice. For that first we will covert, Diameter into radius, then, we will use the formula of volume of Cylinder and then we will find the volume of Jar and glass, and then we will divide, both the volumes, that will give us the number of glasses. Let's do it !

Converting into radius -

$\sf\: Diameter_{(of\: jar)}\: = 30cm$

$\sf\: Radius_{(of\: jar)}\: =\: \sf\dfrac{30}{2}$

$\sf\: Radius_{(of\: jar)}\: = 15cm$

Similarly -

$\sf\: Diameter_{(of\: glasses)}\: = 6cm$

$\sf\: Radius_{(of\: glasses)}\: = \sf\dfrac{6}{2}$

$\sf\: Radius_{(of\: glasses)}\: = 3cm$

Now -

We will find the volumes of each jar and glasses, by using the formula of volume of cylinder.

$\sf \underline{volume \: of \: cylinder} \: = \pi \: {r}^{2} h$

On substituting the values -

$\sf \: v \: = \dfrac{22}{7} \times {(15 \: cm)}^{2} \times 32cm$

$\sf \: v \: = \dfrac{22}{7} \times 225cm \: \times 32cm$

$\sf \: v \: = \dfrac{158400}{7}$

$\sf \: v \: = 22628.57 {cm}^{2}$

Similarly -

$\sf \: v \: = \pi \: {r}^{2} h$

$\sf \: v \: = \: \dfrac{22}{7} \times {(3cm)}^{2} \times 8cm$

$\sf \: v \: = \dfrac{22}{7} \times 9cm \: \times 8cm$

$\sf \: v \: = \dfrac{1584}{7}$

$\sf \: v \: = 226.28 \: {cm}^{2}$

At the end -

We will divide the volumes, from that we will find the number of glasses.

$\sf \: number_{(of\:glasses)}\: = \dfrac{22628.57}{226.28}$

$\sf \: number_{(of\:glasses)} \: = 100 \: glasses \: (approx)$

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