Question

The dimensions of an ellipse are 66cm, 42cm and 21cm respectively. It is melted and recast into the spheres of diameter 4.2 cm. Find the number of sphere formed...​

Answer 1

Number of spheres formed is 785

• It is given that the dimensions of the ellipsoid are 66 cm, 42 cm, 21 cm respectively.
• These are the lengths of axes of the ellipsoid. Now we know an ellipsoid of the form $\frac{x^{2} }{a^{2} } +\frac{y^{2} }{b^{2} } +\frac{z^{2} }{c^{2} } =1$ has the volume $\frac{4}{3}\pi abc$ where a,b,c are the lengths of semi axes.
• So here the semi axes are a= 33 cm , b = 21 cm , c = 10.5 cm. So the volume of the ellipsoid is $\frac{4}{3} \pi *33*21*10.5 = 30479.732$ cubic cm.
• Now this is melted and recasted into spheres with diameter 4.2 cm or radius,r= 2.1 cm
• So volume of each small spheres is $\frac{4}{3} \pi (2.1)^{3} = 38.7924$ cubic cm.
• So number of spheres formed =    $\frac{30479.732}{38.7924} = 785$