Question

In a building there are 24 cylindrical pillars. The radius of each pillar is 42cm and height is 4m.
Find the cost of painting the Curved Surface Area of all the pillars at the rate of rupees 8 per m2

Answer 1

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

Given that,

• Radius of cylindrical pillar, r = 42 cm = 0.42 m

• Height of cylindrical pillar, h = 4 m

We know,

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

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

So, on substituting the values, we get

$\rm \: CSA_{(1\:Cylindrical\:pillar)} \: = \: 2 \times \dfrac{22}{7} \times 0.42 \times 4$

$\rm\implies \:CSA_{(1\:Cylindrical\:pillar)} = 10.56 \: {m}^{2}$

So,

$\rm \: CSA_{(24\:Cylindrical\:pillar)} = 10.56 \times 24$

$\rm\implies \:CSA_{(1\:Cylindrical\:pillar)} = 253.44 \: {m}^{2}$

Now, further given that

$\rm \: Cost\:of\:painting \: {1 \: m}^{2} \: = \: Rs \: 8$

So,

$\rm \: Cost\:of\:painting \: {253.44 \: m}^{2} \: =8 \times 253.44 = Rs \:2027.52$

So,

$\red{\sf\implies Cost\:of\:painting\: CSA_{(24\:Cylindrical\:pillar)} = Rs \: 2027.52}$

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

Additional Information :-

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