Question

The curved surface area and volume of a cylindrical pillar are \[264{{m}^{2}}\]and \[396{{m}^{2}}\] respectively. Find the diameter and height of the pillar.

Answer 1

Hint: So first we will assume its radius as R and height of pillar as h. Now applying the formula of curved surface area of cylinder \[2\pi Rh\] which is given as 264 and applying formula of volume of cylinder \[\pi {{R}^{2}}h\] which is given as 396.
Now we can write it as \[2\pi Rh=264\] and \[\pi {{R}^{2}}h=396\] so we will divide both expression and get the value of R, so our diameter will be 2R.

Complete step by step answer:

Given the curved surface area and volume of a cylindrical pillar are \[264{{m}^{2}}\]and \[396{{m}^{2}}\] respectively and we have to Find the diameter and height of the pillar. So first we will assume its radius as R and height of pillar as h now we know their formulas as
formula of curved surface area of cylinder \[2\pi Rh\] so equating it with \[264{{m}^{2}}\]
we got expression as \[2\pi Rh=264.....(1)\]
similarly formula of volume of cylinder of radius R and Height h is \[\pi {{R}^{2}}h\] so equating it with \[396{{m}^{2}}\], we got expression as \[\pi {{R}^{2}}h=396......(2)\]
now dividing equation (2) by equation (1) we got expression \[\dfrac{\pi {{R}^{2}}h}{2\pi Rh}=\dfrac{396}{264}.\]
which on solving looks like \[\dfrac{R}{2}=\dfrac{3}{2}.\] solving it we got \[R=3\]
So, diameter will be 2R which will be 6
After calculating value of \[R=3\] if we put it in formula of curved surface area of cylinder \[2\pi Rh\] and equating it with \[264{{m}^{2}}\] we got the unknown h, height of pillar
\[2\pi (3)h=264\] which on solving looks \[h=\dfrac{264}{6\pi }\]
so, on solving this we get h (height of pillar) as 14m.

Hence diameter will be 6m and height will be 14m.

Note: In some of the questions it is given that cylinder is closed from both side so now it means we have consider top and bottom area also in our curved surface area so now curved surface area will be \[2\pi Rh+\pi {{R}^{2}}+\pi {{R}^{2}}\]here \[\pi {{R}^{2}}\] is the area of top and similarly \[\pi {{R}^{2}}\]is the area of bottom .