Question

The inner curved surface area of a hemispherical dome of a building needs to be painted. If the circumference of the base is 17.6m, find the cost of painting it at the rate of Rs.5 per sq.m
A.Rs. 246.4
B.Rs. 24.40
C.Rs. 26.40
D.None of these

Answer 1

Hint: To find the cost of painting a hemispherical dome we need to calculate the surface area of the hemispherical dome as the painting rate is given per square meter of their area. So to calculate the area of the dome first calculate the radius of the dome from the given value of the circumference of hemispherical dome. Then with the help of the radius of the hemispherical dome calculate the area then according to the mentioned rate calculate the cost of painting.

Complete step-by-step answer:
We have,
Circumference \[ = 17.6\;\]
Circumference of circle \[ = 2\pi r\]
 \[17.6 = 2 \times \dfrac{{22}}{7} \times r\]
Or,
 \[44r = 17.6 \times 7\]
Or,
 \[r = \dfrac{{123.2}}{{44}} = 2.8\;\]m
Now, Curved surface area of the hemisphere \[ = 2\pi {r^2}\]
on putting the value of radius we get the area of hemispherical dome.
 \[ = 2 \times \dfrac{{22}}{7} \times 2.8 \times 2.8\]
 \[ = 49.28\;\] $m^2$
As given
Cost of painting =Rs. 5 per $m^2$
Total cost of painting = area of dome * rate of painting
 \[ = 49.28 \times 5\]
=Rs. 246.4
Hence the total cost of painting of the hemispherical dome is Rs. 246.4
So, the correct answer is “Rs. 246.4”.

Note: Here in this question it is clearly mentioned that the dome is hemispherical so do not forget this and apply the formula of surface area of the complete sphere which leads to complete wrong answer.