Question

conical bowl of diameter 7cm bowl filled with soup of height 6 cm find how much soup is needed to prepare for 320 patients​

Answer 1

Answer:

Given :-

• A conical bowl of diameter 7 cm bowl filled with soup of height 6 cm.

To Find :-

• How much soup is needed to prepare for 320 patients.

Formula Used :-

$\clubsuit$ Radius Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Radius =\: \dfrac{Diameter}{2}}}}\: \: \: \bigstar$

$\clubsuit$ Volume Of Cone Formula :

$\bigstar \: \: \sf\boxed{\bold{\pink{Volume_{(Cone)} =\: \dfrac{1}{3}{\pi}r^2h}}}\: \: \: \bigstar$

where,

• π = Pie or 22/7
• r = Radius
• h = Height

Solution :-

First, we have to find the radius of a conical bowl :

Given :

• Diameter = 7 cm

According to the question by using the formula we get,

$\leadsto \bf Radius_{[Conical\: Bowl]} =\: \dfrac{Radius}{2}$

So,

$\leadsto \sf Radius_{[Conical\: Bowl]} =\: \dfrac{7}{2}$

$\leadsto \sf\bold{\green{Radius_{[Conical\: Bowl]} =\: 3.5\: cm}}$

Hence, the radius of a conical bowl is 3.5 cm .

Now, we have to find the volume of one conical bowl :

Given :

• Radius = 3.5 cm
• Height = 6 cm

According to the question by using the formula we get,

$\implies \bf Volume_{(Conical\: Bowl)} =\: \dfrac{1}{3}{\pi}r^2h$

$\implies \sf Volume_{(Conical\: Bowl)} =\: \dfrac{1}{3} \times \dfrac{22}{7} \times (3.5)^2 \times 6$

$\implies \sf Volume_{(Conical\: Bowl)} =\: \dfrac{22}{21} \times (3.5 \times 3.5) \times 6$

$\implies \sf Volume_{(Conical\: Bowl)} =\: \dfrac{22}{21} \times 12.25 \times 6$

$\implies \sf Volume_{(Conical\: Bowl)} =\: \dfrac{22}{21} \times 73.5$

$\implies \sf Volume_{(Conical\: Bowl)} =\: \dfrac{1617}{21}$

$\implies \sf\bold{\blue{Volume_{(Conical\: Bowl)} =\: 77\: cm^3}}$

Hence, the volume of one conical bowl is 77 cm³ .

Now, we have to convert cm³ into litres :

$\mapsto \sf Volume_{(Conical\: Bowl)} =\: 77\: cm^3$

$\mapsto \sf Volume_{(Conical\: Bowl)} =\: \dfrac{77}{1000}\: litres$

$\mapsto \sf\bold{\purple{Volume_{(Conical\: Bowl)} =\: 0.077\: litres}}$

Now, we have to find how much soup is needed to prepare for 320 patients :

Given :

• Number of patients = 320 patients
• Volume of one conical bowl = 0.077 litres

According to the question :

$\dashrightarrow \sf 320 \times 0.077$

$\dashrightarrow \sf\bold{\red{24.64\: litres}}$

$\therefore$ The soup needed to prepare for 320 patients is 24.64 litres .

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Answer 2

The volume of one conical bowl is 77 cm³.

Volume of 320 such bowls = 77 × 320

Volume of 320 such bowls = 24640 cm³

Convert cm³ to litres.

1 cm³ = 0.001 l

24640 cm³ = 24.64

24.64 litres of soup is required for 320 patients.

bht shi ignore kr diya :(