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 ₹ 8.50 per sq m.​

Answer 1

$\begin{gathered}\begin{gathered}\bf \:Given-\begin{cases} &\sf{radius_{(cylinderical \: pillar)} = 28 \: cm} \\ &\sf{height_{(cylinderical \: pillar)} = 4 \: m}\\ &\sf{Number \: of \: pillars \: = 24}\\ &\sf{Cost \: of \: painting \: {1 \: m}^{2} = Rs \: 8.50} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \: To \: Find - \begin{cases} &\sf{Cost \: of \: painting \: 24 \: pillars}\end{cases}\end{gathered}\end{gathered}$

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

Given that

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

• Height of cylinderical pillar, h = 4 m

So,

• Curved Surface Area of 1 cylinderical pillar is

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

$\rm :\longmapsto\:CSA_{(cylinderical \: pillar)} = 2 \times \dfrac{22}{7} \times 0.28 \times 4$

$\rm :\longmapsto\:CSA_{(cylinderical \: pillar)} = 7.04 \: {m}^{2}$

$\bf\implies \:CSA_{(24 \: cylinderical \: pillars)} = 7.04 \times 24 = 168.96 \: {m}^{2}$

Now,

$\rm :\longmapsto\:Cost \: of \: painting \: {1 \: m}^{2} = Rs \: 8.50$

$\rm :\longmapsto\:Cost \: of \: painting \: {168.96 \: m}^{2} =8.5 \times168.96 = Rs1436.16$

Additional Information :-

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²