Question

Curved surface area and volume of a cylinder are in the ratio 2:7, find the radius of the cylinder? please army ​

Answer 1

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

Let assume that

• Radius of cylinder be r units

• Height of cylinder be h units

Given that,

$\rm \: CSA_{(Cylinder)} : Volume_{(Cylinder)} \: = \: 2 : 7$

$\rm \: 2\pi \: rh : \pi \: {r}^{2} h \: = \: 2 : 7$

$\rm \: \dfrac{2\pi \: rh}{\pi \: {r}^{2} h} = \dfrac{2}{7}$

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

$\bf\implies \:r \: = \: 7 \: units$

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

Additional Information :-

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

Answer 2

Question:-

• Curved surface area and volume of a cylinder are in the ratio 2:7, find the radius of the cylinder?

To find:-)

• Radius of the cylinder.

Given:-)

• Curved surface area and volume of cylinder in ratio 2:7.

Formula used:-)

$\small\boxed {\bf{ \frac{ \red{Curved \: Surface \: Area_{cylinder}} }{ \green{Volume _{cylinder}} } }}$

Solution:-

Given that:-

$\small\underline{\sf{Curved \: Surface \: Area:Volume=2:7}}$

$\large\underline{\sf{2\pi rh \ratio \pi {r}^{2}h = 2 \ratio 7 }}$

$\large\boxed{\sf{ \implies \frac{2\pi rh}{\pi {r}^{2}h } = \frac{2}{7} }}$

On cross multiplying we get:-

$\large\boxed{\sf{ \implies 7 \times 2\pi rh = 2\pi {r}^{2} h}}$

On cross multiplying we get:-

$\large\boxed{\sf{ \implies \frac{7 \times 2\pi rh}{2\pi {r}^{2} h} }}$

$\large\boxed{\sf{ \implies \frac{7}{r} }}$

On bringing r to RHS we get:-

$\large\boxed{\bf{ \implies 7 = r}}$

Hence, the radius of cylinder is 7.