A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones, each of radius 3.5 cm and height 3 cm.

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 3 cm. How many cones are obtained?

Solution:

Radius of the metallic sphere, = 10.5 cm

Volume of the sphere $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi(10.5)^{3} \mathrm{~cm}^{3}$

Radius of each smaller cone, r2 = 3.05 cm
Height of each smaller cone = 3 cm

Volume of each smaller cone $=\frac{1}{3} \pi r_{2}{ }^{2} h=\frac{1}{3} \pi(3.05)^{2} \times 3 \mathrm{~cm}^{3}$

Number of cones obtained $=\frac{\text { volume of the sphere }}{\text { volume of each smaller cone }}$

$=\frac{\frac{4}{3} \pi r^{3}}{\frac{1}{3} \pi r_{2}^{2} h}$

$=\frac{4 \times 10.5 \times 10.5 \times 10.5}{3.5 \times 3.5 \times 3}$

$=126.006 \approx 126$

∴ 126 cones are obtained.

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now