Question

The largest sphere is carved out of a cube of side 7 cm . Find the volume of the sphere.
(Take pi=3.14)​

Answer 1

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$\bf \scriptsize{The \: diameter \: of \: the \: largest \: sphere \: that \: can \: be \: Carved \: out \: of \: a \: cube } \\ \bf \scriptsize {of \: a \: side \: 7 \: cm \: will \: be \: 7 cm. \: }$

$\bf \scriptsize{ \implies \: Radius \: of \: the \: sphere = r = \frac{7}{2}cm}$

$\bf \scriptsize{ \therefore \: Volume \: of \: the \: sphere = \frac{4}{3}\pi \: r^{3} }$

$\bf{ \tt \scriptsize{ \implies \frac{4}{3} \times \frac{22}{7} \times ( \frac{7}{2})^{3} cm ^{3}}} \\ \\ \tt \scriptsize{ \implies \frac{4}{3} \times \frac{22}{7} \times \frac{7}{2} \times \frac{7}{2} \times \frac{7}{2} cm^{3}} \\ \\ \tt \scriptsize{ \implies \frac{ \cancel4 ^{ \cancel2}}{3} \times \frac{ \cancel22 ^{11} }{ \cancel7} \times \frac{ \cancel7}{ \cancel2} \times \frac{7}{ \cancel2} \times \frac{7}{ \cancel2}} \\ \\ \tt \scriptsize{ \implies \frac{49 \times 11}{3} \: cm ^{3} = \frac{ \cancel{539}}{ \cancel{3}} \: cm^{3} = 179.67 \: cm ^{3} }$

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Answer 2

ThediameterofthelargestspherethatcanbeCarvedoutofacube

ofaside7cmwillbe7cm.

}⟹Radiusofthesphere=r=

2

7

cm

}∴Volumeofthesphere=

3

4

πr

3

⟹

3

4

×

7

22

×(

2

7

)

3

cm

3

⟹

3

4

×

7

22

×

2

7

×

2

7

×

2

7

cm

3

⟹

3

4

2

×

7

2

2

11

×

2

7

×

2

7

×

2

7

⟹

3

49×11

cm

3

=

3

539

cm

3

=179.67cm

3

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