A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume, if its height h and radius r are related by:

Question

A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume, if its height $h$ and radius $r$ are related by:

Smart Achievers · Accepted Answer

(4)

Ans. $h = r$

Explanation:

Surface area, $S = 2 π r h + π r^{2}$ $\dots (i)$

and $V = π r^{2} h$ $\dots (i i)$

From Eq. (i),

$h = \frac{S - π r^{2}}{2 π r}$

From Eq. (ii),

$V = \frac{r}{2} (S - π r^{2})$

$\Rightarrow$ $\frac{d V}{d r} = \frac{1}{2} (S - 3 π r^{2}) = 0$

$\Rightarrow$ $S - 3 π r^{2} = 0$

$\Rightarrow$ $S = 3 π r^{2}$

On putting the value of S in eq. (i), we get

$3 π r^{2} = 2 π r h + π r^{2}$

$\Rightarrow$ $r = h$

Solution

Q.
A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume, if its height $h$ and radius $r$ are related by:

1 $2 h = r$

2 $h = 4 r$

3 $h = 2 r$

4 $h = r$

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Solution

Q. A right circular cylinder which is open at the top and has a given surface area, will have the greatest volume, if its height h and radius r are related by:

1 2h=r

2 h=4r

3 h=2r

4 h=r