Question

The CSA of cylinder of height 7cm is 44cm^2 find the diameter of the base of the cylinder

Answer 1

Answer:

7.483cm

Step-by-step explanation:

Cross Sectional area of a Cylinder = πr²

so r² = 44/π

or r = √14

d = 2r

d = 2√14 = 7.483cm

Answer 2

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

Let assume that radius of cylinder be r cm.

So, Diameter of cylinder, d = 2r cm

Given that,

• Height of cylinder, h = 7 cm

• Curved Surface Area of cylinder = 44 cm^2

We know that

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

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

So, on substituting the values, we get

$\rm \: 2 \times \dfrac{22}{7} \times r \times 7 = 44$

$\rm \: 22 \times (2r) = 44$

$\rm \: d \: = \: \dfrac{44}{22}$

$\rm \: d \: = \: 2$

Hence,

$\color{green}\rm\implies \:\boxed{ \rm{ \:Diameter_{(Cylinder)} = 2 \: cm \: }}$

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

Additional Information :-

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