Question

the curved surface area of a cylinder is 1760cm2 ,its volume 12320cm3 find its radius

Answer 1

$\large\underline{\sf{Solution-}}$

Let assume that

• Radius of cylinder = r cm

• Height of cylinder = h cm

Given that,

• Curved Surface Area of cylinder = 1760 sq. cm

We know, Curved Surface Area of cylinder of radius r and height h is given by

$\boxed{ \rm{ \:CSA_{(Cylinder)} \: = \: 2 \: \pi \: r \: h \: }}$

So, we have

$\rm \: 2 \: \pi \: r \: h \: = \: 1760 \: {cm}^{2} - - - (1)$

Further given that

• Volume of cylinder = 12320 cu. cm

We know, Volume of cylinder of radius r and height h is given by

$\boxed{ \rm{ \:Volume_{(Cylinder)} = \pi \: {r}^{2} \: h \: \: }}$

So, we have

$\rm \: \pi \: {r}^{2} \: h \: = \: 12320 - - - (2)$

On dividing equation (2) by (1), we get

$\rm \: \dfrac{\pi \: {r}^{2} \: h}{2 \: \pi \: r \: h} = \dfrac{12320}{1760}$

$\rm \: \dfrac{r}{2} = 7$

$\rm\implies \:r \: = \: 14 \: cm$

$\rule{190pt}{2pt}$

Additional Information :-

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{ \red{More \: Formulae}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$