Math, asked by moly65, 10 months ago

A cone of height 3cm and radius of base 6cm is made of clay. If we reshape it into a sphere,find the radius of the sphere.

Answers

Answered by Anonymous

Answer:

$\large\bold\red{3\:cm}$

Step-by-step explanation:

Given,

A cone having dimension,

Height, h = 3 cm
Radius of base, r = 6 cm

Let the volume be v

But,

We know that,

$v = \frac{1}{3} \pi {r}^{2} h$

Putting the values,

We get,

$= > v = \frac{1}{3} \pi \times {6}^{2} \times 3 \\ \\ = > v = 36\pi \: {cm}^{3}$

Now,

This cone is reshaped into a sphere.

Let,

The radius of sphere be R

Also,

Let the volume be V

But,

We know that,

$V = \frac{4}{3} \pi {R}^{3}$

But,

The sphere has the same volume as the cone was reshaped.

Therefore,

We get,

$= > \frac{4}{3} \pi {R}^{3} = 36\pi \\ \\ = > {R}^{3} = 36 \times \frac{3}{4} \\ \\ = > {R}^{3} = 9 \times 3 \\ \\ = > {R}^{3} = 27 \\ \\ = > R = \sqrt[3]{27 } \\ \\ = > R = 3$

Hence,

Radius of sphere is 3 cm

Answered by lucky997761

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☆AnswEr :

$\large\bold\red{3\:cm}$

☆Step-by-step explanation:

▶Given,

➡A cone having dimension,

◾Height, h = 3 cm

◾Radius of base, r = 6 cm

◾Let the volume be v

=>But,

☆We know that,

v = $\frac{1}{3} \pi {r}^{2} h$

☆Putting the values,

▶We get,

$\begin{lgathered}= > v = \frac{1}{3} \pi \times {6}^{2} \times 3 \\ \\ = > v = 36\pi \: {cm}^{3}\end{lgathered}$

➡Now,

⬛This cone is reshaped into a sphere.

Let,

☆The radius of sphere be R

Also,

➡Let the volume be V

But,

➡We know that,

V = $\frac{4}{3} \pi {R}^{3}$

But,

☆The sphere has the same volume as the cone was reshaped.

;Therefore,

➡We get,

$\begin{lgathered}= > \frac{4}{3} \pi {R}^{3} = 36\pi \\ \\ = > {R}^{3} = 36 \times \frac{3}{4} \\ \\ = > {R}^{3} = 9 \times 3 \\ \\ = > {R}^{3} = 27 \\ \\ = > R = \sqrt[3]{27 } \\ \\ = > R = 3\end{lgathered}$

[]Hence,[]

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☆Radius of sphere is 3 cm☆

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