Question

15.
12 solid spheres of the same radii are made by melting a solid metallic cylinder of base
diameter 2 cm and height 16 cm. Find the diameter of each sphere,​

Answer 1

Answer:

$\huge \fbox \colorbox{red}{✍ Answer}$

Given ,

• Diameter of cylinder = 2 cm

i.e. radius = r = 1 cm

• Height of cylinder = h = 1- cm

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Let , the diameter of sphere be = D

or , radius of Sphere be = R

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Now,

Volume of cylinder = Volume of 12 sphere

Volume of cylinder = 12× Volume of 1 Sphere

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Therefore,

$= > \pi \times {r}^{2} \times {h}^{2} = 12 \times \frac{4}{3} \pi \times {R}^{3}$

$= > \pi \times 1 \times 16 = 12 \times \frac{4}{3} \pi \times {R}^{3}$

$= > \frac{16\pi}{16\pi} = {R}^{3}$

$= > 1 = {R}^{3}$

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Therefore, the radius of Sphere = 1 cm

Thus , Diameter of sphere = 2 cm

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Answer 2

Step-by-step explanation:

Let , the diameter of sphere be = D

or , radius of Sphere be = R

️‍️

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Now,

Volume of cylinder = Volume of 12 sphere

Volume of cylinder = 12× Volume of 1 Sphere

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Therefore,

\begin{gathered} = > \pi \times {r}^{2} \times {h}^{2} = 12 \times \frac{4}{3} \pi \times {R}^{3} \\ \end{gathered}

=>π×r

2

×h

2

=12×

3

4

π×R

3

\begin{gathered} = > \pi \times 1 \times 16 = 12 \times \frac{4}{3} \pi \times {R}^{3} \\ \end{gathered}

=>π×1×16=12×

3

4

π×R

3

\begin{gathered} = > \frac{16\pi}{16\pi} = {R}^{3} \\ \end{gathered}

=>

16π

16π

=R

3

\begin{gathered} = > 1 = {R}^{3} \\ \end{gathered}

=>1=R

3

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