$504$ cones, each of diameter $3.5\ cm$ and height $3\ cm$, are melted and recast into a metallic sphere, Find the diameter of the sphere and hence find its surface area.

Academic Mathematics NCERT Class 10

Given: 504 cones, each of diameter 3.5 cm and height 3 cm, are melted and recast into a metallic sphere

To do: Find the diameter of the sphere and hence find its surface area.

Solution:

No. of cones $= 504$

Diameter of a cone $= 3.5\ cm$

Radius of the cone, $r = \frac{3.5}{2}=1.75\ cm$

Height of the cone, $h = 3\ cm$

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

$=\frac{1}{3} \pi \times ( 1.75^{2} \times 3$

$=3.0625\pi\ cm^{2}$

Volume of 504 cones $=504\times 3.0635\pi\ cm^{2}$

Let the radius of the new sphere be ‘R’.

Volume of the newly formed sphere$=\frac{4}{3} \pi R^{2}$

Volume of 504 cone$=$Volume of newly formed sphere

$3.0625\pi=\frac{4}{3} \pi R^{2}$

$\Rightarrow \ R^{2} =$

Radius of the new sphere $= 10.5\ cm$

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

48 Views

Kickstart Your Career

Get certified by completing the course

Get Started

Advertisements