Question

A mansion has 12 right cylindrical pillars each having radius 50cm and height 3.5m Find the cost to paint the lateral surface of the pillars at Rs. 20 per square metre.

Answer 1

Hint: We need to find the cost to paint the lateral surface of the pillars at Rs 20 per square metre then we need to find surface area of one pillar and then by unitary method we can find lateral surface area of 12 such pillars multiplication.
Lateral surface area of cylindrical pillar \[ = 2\pi rh\]
Where, \[r = \]radius of the pillar
\[h = \]height of the cylinder
\[\pi = \dfrac{{22}}{7}\]
Lateral surface area of 12 cylindrical pillars
\[ = 12\] (area of 1 pillar)

Complete step by step solution:
Given,
Radius of one cylindrical pillar \[ = 50cm\]
Height of one cylindrical pillar \[ = 3.5m\]

We know
\[
  1m = 100cm \\
  1cm = \dfrac{1}{{100}}m \\
  50cm = \dfrac{{50}}{{100}}m \\
  50cm = 0.5m \\
\]

Let us denote the radius by ‘r’ and height by ‘h’
Hence \[r = 0.5m\,\,and\,\,h = 3.5m\]
Lateral surface area of pillar
\[
   = 2 \times \pi \times r \times 1 \\
   = 2 \times \dfrac{{22}}{7} \times 0.5 \times 3 \\
   = 2 \times \dfrac{{22}}{7} \times \dfrac{5}{{10}} \times \dfrac{{35}}{{10}} \\
   = \dfrac{{22}}{7} \times \dfrac{{35}}{{10}} \\
   = 11{m^2} \\
\]

Lateral surface area of 12 such pillars
\[ = 12 \times \] Lateral surface area of one pillar
\[
   = 12 \times 11 \\
   = 132{m^2} \\
\]

Cost of painting \[1{m^2}\]area \[ = Rs\,20\]
Cost of painting \[132\,{m^2} = Rs20 \times 132\]
\[ = Rs\,2640\]

Note: Cylinder is one of the basic shapes, in Mathematics, which has two parallel circular bases at a distance (called height of cylinder). LPG gas-cylinder is one of the real-life examples. It is a three-dimensional shape having surface area and volume. The total area of the cylinder is equal to the sum of its curved surface area and area of the two circular bases.
We can see that cost is given in meters. Hence convert all the units in metre only.