CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A solid sphere of radius $$15\ cm$$ is melted and react into solid right circular cones of radius $$2.5\ cm$$ and height $$8\ cm$$. Calculate the number of cones recast.


Solution

Radius of a solid sphere, $$r=15\ cm$$

Volume of a solid sphere $$=\displaystyle\frac{4}{3}\pi r^3$$

$$=\displaystyle\frac{4}{3}\times \pi (15)^3\ cm^3$$.

Now, radius of right circular cone $$=2.5\ cm$$
 and height, $$h=8\ cm$$.

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

$$=\displaystyle\frac{1}{3}\pi (2.5)^2\times 8$$

$$\therefore$$ The number of cones $$=\displaystyle\frac{\text{Volume of a sphere}}{\text{Volume of a cone}}$$

$$=\displaystyle\frac{\displaystyle\frac{4}{3}\pi \times (15)^3}{\displaystyle\frac{1}{3}\pi (2.5)^2\times 8}$$

$$=\displaystyle\frac{15\times 15\times 15}{2.5\times 2.5\times 2}$$

$$=270$$.

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image