Question

a cone of height 24 cm and radius of base 6 cm is made up of modelling clay.a child reshapes it in the form of a sphere .find the radius of the sphere.i know the answer but plz give a proper explanation.​

Answer 1

$\sf {\large{Question: }}$

$\begin{gathered} \sf{ \green{A \: Cone \: of \: Height \: 24 \: cm \: and \: Radius \: of \: Base \: 6 \: cm}} \\ \sf{ \red{is \: made \: up \: of \: modelling \: clay \: a \: child \: Reshapes \: it}} \\ \sf{ \blue{in \: the \: form \: of \: a \: Sphere.}} \\ \sf{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: find \: the \: radius \: of \: the \: sphere ?}}\end{gathered}$

$\sf{ \large{Method \: of \: Solution:}}$

$\sf{ \pink{Given}}$

$\begin{gathered} \implies{ \sf{ \blue{Height \: of \: the \: cone \: = 24cm}}} \\ \\ \implies{ \sf{ \green{ Radius \: \: of \: the \: cone \: = 6cm}}} \\ \\ \\ \implies{ \sf{ \red {Volume \: of \: the \: cone = \frac{1}{3} \times \frac{22}{7} \times ( {6}^{2} )\times 24}}} \\ \\ \\ \implies{ \sf{ \red {Volume \: of \: the \: cone = 905.14cm}}}\end{gathered}$

$\sf{ \fbox{ \pink{According \: to \: the \: Question:}}}$

$\sf{\red{Volume \: of \: the \: Sphere \: = \frac{3}{4} \times \frac{22}{7} \times ({r}^{3})}}$

$\sf{\purple{Volume \: of \: the \: Sphere \: = \frac{3}{4} \times \frac{3}{4} \times ({r}^{3})=905.14}}$

$\begin{gathered}\sf{\green{Volume \: of \: the \: Sphere \: = \frac{3}{4} \times \frac{22}{7} \times ({r}^{3})=905.14}} \\ \\ \sf{\red{Volume \: of \: the \: Sphere \: = \frac{66}{28} \times ( {r}^{3} ) = 905.14 }} \\ \\ \\ \sf{\green{Volume \: of \: the \: Sphere = {r}^{3} {\implies \: 216}}} \\ \\ \\ \sf{\blue{Volume \: of \: the \: Sphere = (r) {\implies 6cm}}}\end{gathered}$

$\sf{ \red{ \fbox{Hence, \: Required}}} \sf{ \green{ \fbox{ Radius \: of \: Sphere}}} \sf{ \blue{ \fbox{ = 6cm}}}$

Answer 2

Answer:

\sf {\large{Question: }}Question:

\begin{gathered}\begin{gathered} \sf{ \green{A \: Cone \: of \: Height \: 24 \: cm \: and \: Radius \: of \: Base \: 6 \: cm}} \\ \sf{ \red{is \: made \: up \: of \: modelling \: clay \: a \: child \: Reshapes \: it}} \\ \sf{ \blue{in \: the \: form \: of \: a \: Sphere.}} \\ \sf{ \blue{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: find \: the \: radius \: of \: the \: sphere ?}}\end{gathered}\end{gathered}

AConeofHeight24cmandRadiusofBase6cm

ismadeupofmodellingclayachildReshapesit

intheformofaSphere.

findtheradiusofthesphere?

\sf{ \large{Method \: of \: Solution:}}MethodofSolution:

\sf{ \pink{Given}}Given

\begin{gathered}\begin{gathered} \implies{ \sf{ \blue{Height \: of \: the \: cone \: = 24cm}}} \\ \\ \implies{ \sf{ \green{ Radius \: \: of \: the \: cone \: = 6cm}}} \\ \\ \\ \implies{ \sf{ \red {Volume \: of \: the \: cone = \frac{1}{3} \times \frac{22}{7} \times ( {6}^{2} )\times 24}}} \\ \\ \\ \implies{ \sf{ \red {Volume \: of \: the \: cone = 905.14cm}}}\end{gathered}\end{gathered}

⟹Heightofthecone=24cm

⟹Radiusofthecone=6cm

⟹Volumeofthecone=

3

1

×

7

22

×(6

2

)×24

⟹Volumeofthecone=905.14cm

\sf{ \fbox{ \pink{According \: to \: the \: Question:}}}

According to the Question:

\sf{\red{Volume \: of \: the \: Sphere \: = \frac{3}{4} \times \frac{22}{7} \times ({r}^{3})}}VolumeoftheSphere=

4

3

×

7

22

×(r

3

)

\sf{\purple{Volume \: of \: the \: Sphere \: = \frac{3}{4} \times \frac{3}{4} \times ({r}^{3})=905.14}}VolumeoftheSphere=

4

3

×

4

3

×(r

3

)=905.14

\begin{gathered}\begin{gathered}\sf{\green{Volume \: of \: the \: Sphere \: = \frac{3}{4} \times \frac{22}{7} \times ({r}^{3})=905.14}} \\ \\ \sf{\red{Volume \: of \: the \: Sphere \: = \frac{66}{28} \times ( {r}^{3} ) = 905.14 }} \\ \\ \\ \sf{\green{Volume \: of \: the \: Sphere = {r}^{3} {\implies \: 216}}} \\ \\ \\ \sf{\blue{Volume \: of \: the \: Sphere = (r) {\implies 6cm}}}\end{gathered}\end{gathered}

VolumeoftheSphere=

4

3

×

7

22

×(r

3

)=905.14

VolumeoftheSphere=

28

66

×(r

3

)=905.14

VolumeoftheSphere=r

3

⟹216

VolumeoftheSphere=(r)⟹6cm

\sf{ \red{ \fbox{Hence, \: Required}}} \sf{ \green{ \fbox{ Radius \: of \: Sphere}}} \sf{ \blue{ \fbox{ = 6cm}}}

Hence, Required

Radius of Sphere

= 6cm