Question

The curved surface area of a cylindrical pillarvis 440cm square and it's volume is 1520cm cube. Find the height of the pillar.​

Answer 1

$\huge{\red{\underline{\underline{\rm{Answer:}}}}}$

$\star{\underline{\green{\sf{Given:}}}}$

$\sf{\implies CSA\;of\;cylindrical\;Pillar=440\;cm^{2}}$

$\sf{\implies Volume\;of\;cylindrical\;pillar=1520\;cm^{3}}$

$\star{\underline{\green{\sf{Formula\;used:}}}}$

${\sf{\implies CSA\;of\;cylinder=2\pi rh}}$

$\sf{\implies Volume\;of\;cylinder=\pi r^{2}h}$

$\star{\underline{\green{\sf{To\;Find:}}}}$

$\sf{\implies Height\;of\;the\;pillar.}$

$\textsf{Now, let 'r' be the radius and 'h' be the height of the cylindrical pillar.}$

${\sf{\implies CSA\;of\;cylinder=2\pi rh}}$

${\sf{\implies 440\;cm^{2}=2\pi rh}\;\;\;\;.........(1)}$

$\sf{\implies Volume\;of\;cylinder=\pi r^{2}h}$

$\sf{\implies 1520\;cm^{3}=\pi r^{2}h\;\;\;\;\;..........(2)}$

$\textsf{Now, divide Equation (2) by Equation (1), we get.}$

$\sf{\implies \dfrac{1520}{440}=\dfrac{\pi r^{2}h}{2\pi rh}}$

$\sf{\implies 3.45=\dfrac{r}{2}}$

$\sf{\implies r=6.90\;cm}$

$\textsf{Now, put the value of 'r' in Equation (1), we get}$

${\sf{\implies 440\;cm^{2}=2\pi rh}\;\;\;\;.........(1)}$

$\sf{\implies 440=2\times \dfrac{22}{7}\times 6.90\times h}$

$\sf{\implies 440=\dfrac{44}{7}\times 6.90\times h}$

$\sf{\implies 440 = \dfrac{304}{7}\times h}$

$\sf{\implies 3080=304\times h}$

$\sf{\implies h=\dfrac{3080}{304}}$

$\sf{\implies h = 10.13\;cm\;\;\;\;(Approx)}$

Hence, Height of the pillar is 10.13 cm.

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Height of the cylindrical pillar is 10.15 cm.

$\bold{\underline{\underline{\large{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• The curved surface area of a cylindrical pillar is 440 cm square
• Volume of the cylindrical pillar is 1520 cm cube.

To FiNd :

• Height of the pillar

SoLuTioN :

First let's calculate the radius of the cylindrical pillar.

Dividing the curved surface area of the cylindrical pillar by volume of the cylindrical pillar will give us the radius.

Curved surface area :

Using the formula :

$\bold{\large{\boxed{\tt{\green{\sf{CSA\:=\:2\:\pi\:rh}}}}}}$

Where,

• r = radius
• h = height

Block in the available values,

$\hookrightarrow$ $\sf{440\:=\:2\:\pi\:r\:h}$

$\hookrightarrow$ $\sf{\dfrac{440}{2}\:=\:\pi\:rh}$

$\hookrightarrow$ $\sf{220\:=\:\pi\:rh}$ -----> (1)

Volume :

Using the formula :

$\bold{\large{\boxed{\tt{\green{\sf{Volume\:=\:\pi\:r^2h}}}}}}$

Block in the available values,

$\hookrightarrow$ $\sf{1520\:=\:\pi\:r^2\:h}$ ----> (2)

Divide, volume by curved surface area.

$\hookrightarrow$ $\sf{\dfrac{\pi\:r^2h\:=\:1520}{\pi\:rh\:=\:220}}$

$\hookrightarrow$ $\sf{r\:=\:6.90\:cm}$

$\sf{\therefore{Radius\:of\:the\:cylindrical\:pillar\:=\:6.90\:cm}}$

We can now substitute value of radius in any of the above equation and can easily calculate the height.

Substituting r = 6.90 in the volume of the cylindrical pillar,

$\hookrightarrow$ $\sf{1520\:=\:\pi\:r^2\:h}$

$\hookrightarrow$ $\sf{1520\:=\:{\dfrac{22}{7}\:(6.90)^2\:h}}$

$\hookrightarrow$ $\sf{1520\:=\:{\dfrac{22}{7}\:6.90\:\times\:6.90\:\times\:h}}$

$\hookrightarrow$ $\sf{1520\:=\:{\dfrac{22}{7}\:\times\:47.61\:\times\:h}}$

$\hookrightarrow$ $\sf{1520\:=\:{\dfrac{1047.42}{7}\:\times\:h}}$

$\hookrightarrow$ $\sf{1520\:\times\:7\:=\:1047.42\:\times\:h}$

$\hookrightarrow$ $\sf{10640\:=\:1047.42\:\times\:h}$

$\hookrightarrow$ $\sf{\dfrac{10640}{1047.42\:=\:h}}$

$\hookrightarrow$ $\sf{10.15\:cm}$

$\sf{\therefore{Height\:of\:the\:cylindrical\:pillar\:=\:10.15\:cm}}$