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Question
If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is ______.
Options
`2pi"h"^2`
`3/2 pi"h"^2`
`4/3 pi"h"^2`
`pi"h"^2`
Solution
If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is `bb(3/2 pih^2)`.
Explanation:
Let r be the radius of the cylinder and h be its height.
It is given that:
`2"r" = "h" ⇒ "r" = "h"/2`
Therefore, total surface area S is:
`"S"=2pi "r"^2 + 2 pi "rh"`
`⇒ "S" = 2pi "r" ("r" +"h")`
`⇒ "S" = 2pi xx "h"/2 ("h"/2 +"h")`
`⇒ "S" = (3pi"h"^2)/2`
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