Question

10 cylindrical pillars of the building have to be painted. The diameter of each pillar is $70$ cm and the height is 4 m. What is the cost of painting at the rate of 5 per square meter?
A. Rs. 400
B. Rs. 440
C. Rs. 480
D. Rs. 500

Answer 1

Hint: We have to find the cost of painted 10 cylindrical pillars at the rate of 5 per square meter.
Here the diameter of the pillar is given so we can find the radius by dividing the diameter by two.
Next, apply the formula of the curved surface area of the cylinder that is, $2\pi rh$ .
Here, r is the radius and h is the height.
Next, find the curved surface area of 10 pillars by multiplying $2\pi rh$ by 10.
Multiply the surface area by the rate of per square meter which is given as 5 per square meter.

Complete step-by-step solution:
Consider the 10 cylindrical pillars of the building that have to be painted.
The diameter d of the pillar is 70 cm.
Determine the radius r of the pillar,
$r={\displaystyle \frac{d}{2}}$
$r={\displaystyle \frac{70}{2}}$
$r=35$ cm
Convert centimeter to meter,
$r={\displaystyle \frac{35}{100}}$ m
The height of the pillar is $4$ m.
Determine the surface area of each cylindrical pillar;
Surface Area of the cylinder=$2\pi rh$, r is the radius, and h is the height.
The surface area of 10 cylindrical pillars=$10\times 2\pi rh$
The cost of painting per square meter is 5 Rs.
The cost of painting the surface area $10\times 2\pi rh$ is, $5\times 10\times 2\pi rh$.
Substitute $r=35$ cm, $\pi ={\displaystyle \frac{22}{7}}$ and $h=4$ cm into $5\times 10\times 2\pi rh$.
The cost of painting of surface =$5\times 10\times 2\times {\displaystyle \frac{22}{7}}\times {\displaystyle \frac{35}{100}}\times 4$
The cost of the painting of the surface =$440$Rs.

Option B is the correct answer.

Note: The diameter of the cylindrical pillar is in cm and the height is in meter so don’t forget to change centimeter to the meter.