Question

A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones, each of radius 3.5 cm and height is 3 cm. How many cones are obtained ?
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Answer 1

Answer:

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Step-by-step explanation:

Volume of sphere melted= 4/3  πR ^3=4/3π×10.5 ^3

 

Volume of each cone formed =   1/3 πr^2 h=  1/3 π×(3.5) ^2 ×3

∴ Number of cones obtained =$\frac{Volumeofeachconeformed}{Volumeofthespheremelted}$

=$\frac{( 4/3)\pi *(10.5) ^3}{(1/3)*\pi *(3.5)^2*3}$= 126

Answer 2

S O L U T I O N :

$\underline{\bf{Given\::}}$

• Radius of metallic sphere, (r) = 10.5 cm = 21/2 cm
• Radius of each cone, (r) = 3.5 cm = 7/2 cm
• Height of each cone, (h) = 3 cm

$\underline{\bf{Explanation\::}}$

As we know that formula of the volume of sphere;

$\boxed{\bf{Volume = \frac{4}{3} \pi r^{3}}}$

A/q

$\mapsto\tt{Volume \:of\:sphere = \dfrac{4}{3} \pi r^{3}}$

$\mapsto\tt{Volume \:of\:sphere =\bigg( \dfrac{4}{3} \pi \times \dfrac{21}{2} \times \dfrac{21}{2} \times \dfrac{21}{2} \bigg)}$

$\mapsto\tt{Volume \:of\:sphere =\bigg( \dfrac{\cancel{4}}{\cancel{3}} \pi \times \dfrac{\cancel{21}}{\cancel{2}} \times \dfrac{21}{\cancel{2}} \times \dfrac{21}{2} \bigg)}$

$\mapsto\tt{Volume \:of\:sphere =\bigg(\dfrac{3087}{2} \pi \bigg)cm^{3}}$

&

As we know that formula of the volume of cone;

$\boxed{\bf{Volume\:of\:cone = \frac{1}{3} \pi r^{2} h}}$

So,

$\mapsto\tt{ Volume\:of\:cone = \frac{1}{3} \pi r^{2} h}$

$\mapsto\tt{Volume \:of\:cone =\bigg( \dfrac{1}{3} \pi \times \dfrac{7}{2} \times \dfrac{7}{2} \times 3 \bigg)}$

$\mapsto\tt{Volume \:of\:cone =\bigg( \dfrac{1}{\cancel{3}} \pi \times \dfrac{7}{2} \times \dfrac{7}{2} \times \cancel{3} \bigg)}$

$\mapsto\tt{Volume \:of\:cone =\bigg( \dfrac{1}{1} \pi \times \dfrac{7}{2} \times \dfrac{7}{2} \bigg)}$

$\mapsto\tt{Volume \:of\:cone =\bigg( \dfrac{49 \pi}{4}\bigg)cm^{3}}$

Now,

Required number of cones :

$\longrightarrow\tt{\dfrac{Volume \:of\:the\:sphere }{Volume\:of\:each\:cone } }$

$\longrightarrow\tt{\dfrac{\dfrac{3087}{2}\pi }{\dfrac{49 \pi }{4} } }$

$\longrightarrow\tt{\dfrac{3087\pi}{2} \times \dfrac{4}{49 \pi} }$

$\longrightarrow\tt{\dfrac{\cancel{3087\pi}}{\cancel{2}} \times \dfrac{\cancel{4}}{\cancel{49 \pi}} }$

$\longrightarrow\tt{63 \times 2 }$

$\longrightarrow\bf{126\:cones }$

Thus,

The 126 cones will obtained .