Question

$\large\underbrace{\bf{ \red{Question}}}$

In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m. Find the total cost of painting the curved surface area of all pillars at the rate of ₹8 per m².

Make sure about units in each step.
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Answer 1

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

Given that,

• In a building there are 24 cylindrical pillars. The radius of each pillar is 28 cm and height is 4 m.

So,

• Radius of cylindrical pillar, r = 28 cm = 0.28 m

• Height of cylindrical pillar, h = 4 m

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

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

So, using this result, we have

$\rm \: CSA_{(1 \: pillar)} \: = \: 2 \: \pi \: r \: h \: \:$

$\rm \: = \: 2 \times \dfrac{22}{7} \times 0.28 \times 4$

$\rm \: = \: 2 \times \dfrac{22}{7} \times \dfrac{28}{100} \times 4$

$\rm \: = \: 2 \times 22 \times \dfrac{4}{100} \times 4$

$\rm \: = \: 7.04 \: {m}^{2}$

So,

$\rm \: CSA_{(24\: pillar)} \: = \:7.04 \times 24 \: = \: 168.96 \: {m}^{2}$

Now, further given that

Cost of painting the curved surface area per m² = ₹ 8

So,

Cost of painting the curved surface area 168.96 m² = 168.96 × 8 = ₹ 1351.68

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

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

Answer:

C.S.A. of cylindrical =2πrh

⇒ C.S.A. of are pillar =2×22×28×4 = 704cm {}^{2}

⇒ C.S.A of 24 pillars =24×704=16896cm

{}^{2}

=16896×10-^{4} m {}^{2}

=1.69m {}^{2}

⇒ Total cost Rs.8×1.69=Rs.13.52