Question

if the curved surface area of a solid right circular cylinder of height H and radius R is one third of its total surface area then find h

Answer 1

$\textsf{Concept:}$

$\textsf{Curved surface area of cylinder=}\mathsf{2\,\pi\,r\,h}\textsf{ square units}$

$\textsf{Total surface area of cylinder=}\mathsf{2\,\pi\,r(h+r)}\textsf{ square units}$

$\textsf{Given:}$

$\textsf{Curved surface area=}\mathsf{\frac{\textsf{Total surface area}}{3}}$

$\implies\mathsf{2\,\pi\,r\,h=\frac{2\,\pi\,r(h+r)}{3}}$

$\implies\mathsf{h=\frac{h+r}{3}}$

$\implies\mathsf{3h=h+r}$

$\implies\mathsf{2h=r}$

$\implies\boxed{\mathsf{h=\frac{r}{2}}}$

Answer 2

curved surface area of cylinder = 2πrh sq. unit

total surface area of cylinder = 2πr(h+r) sq. unit

given:

curved surface area =total surface area /3

2πrh = 2πr(h+r)/3

h = h+r/3

3h = h+r

2h = r

h = r/2

thanks dear ❤️❤️❤️