The ratio of the surface area of a cylinder to the surface area of a sphere is
, that is mentioned in option E.
Step-by-step explanation:
The given is,
Cylinder and sphere has same area.
Step: 1
Formula for surface area of cylinder,
.............................(1)
Where, r - Radius of cylinder
h - Height of cylinder
Step:2
Formula for surface area of sphere,
.......................................(2)
Where, r - Radius of sphere
Step:3
Ratio of the surface area of a cylinder to the surface area of a sphere,
![= \frac{Surface area of cylinder}{Surface area of sphere}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7BSurface%20area%20of%20cylinder%7D%7BSurface%20area%20of%20sphere%7D)
![=\frac{ 2\pi rh + 2\pi r^{2} }{ 4\pi r^{2}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%20%20%202%5Cpi%20rh%20%2B%202%5Cpi%20r%5E%7B2%7D%20%7D%7B%20%20%20%204%5Cpi%20r%5E%7B2%7D%7D)
![= \frac{2\pi r h }{ 4\pi r^{2}} + \frac{ 2\pi r^{2} }{4\pi r^{2}}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2%5Cpi%20r%20h%20%7D%7B%204%5Cpi%20r%5E%7B2%7D%7D%20%2B%20%5Cfrac%7B%202%5Cpi%20%20r%5E%7B2%7D%20%20%20%20%20%7D%7B4%5Cpi%20r%5E%7B2%7D%7D)
![= \frac{ h }{ 2 r} + \frac{ 1 }{2}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%20h%20%7D%7B%202%20r%7D%20%2B%20%5Cfrac%7B%201%20%20%20%20%20%7D%7B2%7D)
![= \frac{2h + 2r}{(2r)(2)}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2h%20%2B%202r%7D%7B%282r%29%282%29%7D)
![= \frac{2(r + h)}{2 (2r)}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B2%28r%20%2B%20h%29%7D%7B2%20%282r%29%7D)
![= \frac{r + h}{2r}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7Br%20%2B%20h%7D%7B2r%7D)
Ratio of the surface area of a cylinder to the surface area of a sphere
.
Result:
The ratio of the surface area of a cylinder to the surface area of a sphere is
, that is mentioned in option E.