Question

a cone and a hemishphere have equal bases and equal total surface area find the ratio of thier hight​

Answer 1

Answer:

$\text{Ratio of their height is}\:\bf{\sqrt3:1}$

Step-by-step explanation:

A cone and a hemishphere have equal bases and equal total surface area find the ratio of thier height

$\text{since the cone and the hemisphere have equal bases, they have the same radius}$

$\text{Let r,h and l be the radius, height and slant height of the cone respectively}$

$\text{As per given data}$

$\pi\:r(l+r)=3\pi\:r^2$

$\implies\:l+r=3r$

$\implies\:l=3r-r$

$\implies\:l=2r$

$\text{We know that,}$

$l^2=h^2+r^2$

$\implies\:(2r)^2=h^2+r^2$

$\implies\:h^2=3r^2$

$\implies\:h=\sqrt3\:r$

$\frac{\text{Height of the cone}}{\text{Height of the hemisphere}}$

$=\frac{\sqrt3\:r}{r}$

$=\frac{\sqrt3}{1}$

$\therefore\:\text{Ratio of their height is}\:\bf{\sqrt3:1}$