Question

A mettalic sphere of radius 10.5 cm is mealted and then recast into small cones ,each of radius 3.5 cm smd height 3cm find how many cones are obtained

Answer 1

Answer:

Solid metallic sphere is melted in to smaller number of cones.

Volume of sphere is  

4/3 π r³= 4/3 π (10.5)³

Volume of one cone 1/3 π r²h

1/3 π (3.5)² 3

Vol of n cones= n x 1/3 π (3.5)² 3

4/3 π (10.5)³ =n x 1/3 π (3.5)² 3

n=4 (10.5)² 3 (2)³/3 x 3

126 cubes

Answer 2

$\textbf{\huge{ANSWER:}}$

$\sf{Given:}$

Radius of the big metallic sphere = 10.5 cm

Radius of the small cone formed by recasting the big metallic sphere = 3.5 cm

Height of the cone formed = 3 cm

$\sf{To\:Find:}$

The number of cones formed from the big metallic sphere

$\sf{Solution:}$

To find the number of cones formed, we need to find the ratio between the Volume of the big metallic sphere and the small cone. The formula will be :-

Number of cones = $\tt{\frac{Volume\:of\:big\:sphere}{Volume\:of\:small\:cone}}$

Volume of the big sphere = $\frac{4}{3} \pi r^{3}$

=》 $\tt{\frac{4}{3}\times\frac{22}{7}\times10.5^{2}}$

=》 $\tt{\boxed{4851 cm^{3}}}$

Volume of the small cone = $\frac{1}{3}\pi r^{2} h$

=》 $\tt{\frac{1}{3}\times\frac{22}{7}\times3.5^{2}\times3}$

=》 $\tt{\boxed{38.5 cm^{3}}}$

Number of cones = $\frac{4851}{38.5}$

=》 $\tt{\boxed{\boxed{126}}}$