Question

i) A right circular cone is $5.8cm$ high and radius of its base is $3.4cm$. It is melted and recast into a right circular cone with radius of its base $1.7cm$. Find its height.

ii) Find the weight of a solid cone whose base is of diameter $42cm$ and vertical height $20cm$

Answer 1

By melting and recasting , volume of

both cones remain same

$\Rightarrow \frac{1}{3}\pi r_1^2{h}_1=\frac{1}{3}\pi r_2^2{h}_2$

$\Rightarrow r_1^2{h}_1=r_2^2{h}_2$

$\Rightarrow h_2=h_1(\frac{r_1}{r_2}{)}^2=5.8\times (\frac{3.4}{1.7}{)}^2$

$\Rightarrow h_2=5.8\times 4=23.2cm$

Volume of given cone $=\frac{1}{3}\pi (21{)}^2\times 20$

$=\frac{1}{3}\times \frac{22}{7}\times 21\times 21\times 20$

$=9240c{m}^2$

For its mass, density is required as mass = density $\times$ volume.