Question

13] A cone of height 24cm and radius 6cm is made up of clay. A child reshapes it in the form of sphere. Find
radius of the sphere​

Answer 1

AnswEr :

⋆ Refer to the Attachment for information :

• Radius of Cone ( r ) = 6 cm
• Height of Cone ( h ) = 24 cm
• Radius of Sphere ( R ) = ?

given that child reshapes the Cone into sphere, therefore there Volume will be Equal.

⇒ Volume of Cone = Volume of Sphere

⇒ 1 /3 πr²h = 4 /3 πR³

⇒ r²h = 4R³

• Plugging the Values

⇒ ( 6 )² × 24 = 4 × R³

⇒ ( 6 )² × 24 /4 = R³

⇒ ( 6 )² × 6 = R³

⇒ ( 6 )³ = R³

• Cancelling Cubes

⇒ R = 6 cm

∴ Radius of the Sphere will be 6 cm.

Answer 2

$\bold{Given}\begin{cases}\sf{Cone\:Height=24cm}\\\sf{Cone\:radius=6cm}\\\sf{radius\:of\:sphere=?}\end{cases}$

$\LARGE\underline{\underline{\sf \red{S}\blue{o}\green{l}\orange{u}\pink{t}\purple{i}\orange{o}\red{n}:}}$

we know That ,

volume of Cone = $\large\red{\boxed{\sf</strong><strong> </strong><strong>\frac{1}{3}</strong><strong>\pi \: {r}^{2} h</strong><strong>}}$

And,

Volume of Sphere = $\large\</strong><strong>g</strong><strong>r</strong><strong>e</strong><strong>e</strong><strong>n</strong><strong>{\boxed{\sf</strong><strong> </strong><strong>\frac{4}{3} \pi \times {</strong><strong>R</strong><strong>}^{3}</strong><strong>}}$

$\textbf{</strong><strong>since</strong><strong> </strong><strong>cone</strong><strong> </strong><strong>is</strong><strong> </strong><strong>reshapes</strong><strong> </strong><strong>into</strong><strong> </strong><strong>sphere</strong><strong>}$

$\textbf{</strong><strong>Their</strong><strong> </strong><strong>Volume</strong><strong> </strong><strong>will</strong><strong> </strong><strong>be</strong><strong> </strong><strong>Same</strong><strong>}$

$\rule{200}{</strong><strong>2</strong><strong>}$

Comparing Volume Now,

$\frac{1}{3} \pi \: {r}^{2} h \: = \frac{4}{3} \pi \times \: {R}^{3} \\ \\ putting \: values \: now \: \\ \\{6}^{2} \times \cancel24 = \cancel4 \times {R}^{3} \\ \\ {6}^{3} = {R}^{3} \:$

So, Radius of Sphere Formed is :-----

$\bold{\boxed{\huge{\boxed{\orange{\small{\boxed{\huge{\red{\bold{\:</strong><strong>R</strong><strong>=</strong><strong>6</strong><strong>c</strong><strong>m</strong><strong>}}}}}}}}}}$