Question

The radius of a solid metalic sphere is 10 CM. It is melted and recost in to small cones of height 10cm and base radius 5cm. find the number of small cone formed​

Answer 1

Answer:

$\huge \fbox \colorbox{red}{Question:-}$

• The radius of a solid metalic sphere is 10 CM. It is melted and recost in to small cones of height 10cm and base radius 5cm. find the number of small cone formed

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$\huge \fbox \colorbox{lime}{SOLUTION ⤵}$

Given :-

• Radius of solid sphere = r = 10 cm
• Radius of cone = R = 5 cm
• Height of cone = 10 cm

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Let the number of cone be 'x' .

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Now :-

• As we know,

$Volume \: of \: sphere = \pink{ \frac{4}{3} \pi {r}^{3} }$

And,

$Volume \: of \: cone = \pink{\frac{1}{3} \pi {R}^{2} h}$

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ACC. to Question :-

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Volume of sphere = number of cone × volume of each cone

$= > \frac{ 4}{3} \pi {r}^{3} = n \times \frac{1}{3} \pi {R}^{2} h$

$= > 4 \times {10}^{3} = n \times {5}^{2} \times 10$

$= > n = \frac{4 \times {10}^{3} }{ {5}^{2} \times 10 }$

$= > n = \frac{4000}{250}$

$= > n = 16$

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Therefore , the number of cone = 16

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Answer 2

Answer:

Answer:

\huge \fbox \colorbox{red}{Question:-}

Question:-

The radius of a solid metalic sphere is 10 CM. It is melted and recost in to small cones of height 10cm and base radius 5cm. find the number of small cone formed

️‍️

️‍️

\huge \fbox \colorbox{lime}{SOLUTION ⤵}

SOLUTION ⤵

Given :-

Radius of solid sphere = r = 10 cm

Radius of cone = R = 5 cm

Height of cone = 10 cm

️‍️

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Let the number of cone be 'x' .

️‍️

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Now :-

As we know,

\begin{gathered}Volume \: of \: sphere = \pink{ \frac{4}{3} \pi {r}^{3} } \\ \end{gathered}

Volumeofsphere=

3

4

πr

3

And,

\begin{gathered}Volume \: of \: cone = \pink{\frac{1}{3} \pi {R}^{2} h} \\ \end{gathered}

Volumeofcone=

3

1

πR

2

h

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ACC. to Question :-

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Volume of sphere = number of cone × volume of each cone

\begin{gathered} = > \frac{ 4}{3} \pi {r}^{3} = n \times \frac{1}{3} \pi {R}^{2} h \\ \end{gathered}

=>

3

4

πr

3

=n×

3

1

πR

2

h

\begin{gathered} = > 4 \times {10}^{3} = n \times {5}^{2} \times 10 \\ \end{gathered}

=>4×10

3

=n×5

2

×10

\begin{gathered} = > n = \frac{4 \times {10}^{3} }{ {5}^{2} \times 10 } \\ \end{gathered}

=>n=

5

2

×10

4×10

3

\begin{gathered} = > n = \frac{4000}{250} \\ \end{gathered}

=>n=

250

4000

= > n = 16=>n=16

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Therefore , the number of cone = 16

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