A hemi-spherical dome of a building needs to be painted. IF the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5 per 100 cm².
Answers
Rs. 24640 is the cost of painting it, given the cost of painting is Rs. 5 per 100 cm².
From given we have,
The circumference of the base of the dome is 17.6 m
The cost of painting is Rs. 5 per 100 cm²
Circumference of base = 2πr = 17.6 cm
2 × 22/7 × r = 17.6
r = (17.6 × 7) / (2 × 22)
r = 2.8 m
Area to be painted = curved surface area of hemisphere
CSA = 2πr^2
= 2 × 22/7 × 2.8^2
= 49.28 m^2
= 492800 cm^2
Therefore the cost of painting = 492800 cm^2 × Rs. 5 per 100 cm^2
= 492800 × 5/100
= 4928 × 5
= Rs. 24640
Given:-
- The circumference of the base of the dome is 17.6 m, The cost of painting is Rs. 5 per 100 cm².
To find:-
- Find the cost of painting ...?
Solutions:-
- The circumference of the base of the dome is 17.6 m.
Circumference of circle = 2πr
=> 2πr = 17.6
=> 2 × 22/7 = 17.6
=> 44/7 × r = 17.6
=> r = 17.6 × 7/44
=> r = 0.4 × 7
=> r = 2.8
The surface area of the hemisphere dome surface area = 2πr²
=> 2 × 22/7 × 2.8 × 2.8
=> 2 × 22 × 0.4 × 2.8
=> 49.28
The curved surface area of the dome is 49.28m².
Since, the rate of the painting in cm² to convert the surface area from m² to cm².
Curved surface area = (49.28 × 10000) cm²
= 492800cm²
Now,
The rate of painting per 100cm² = Rs. 5.
The rate of painting per 1cm² = 5/100
So, the cost of painting the dome = 5/100 × 492800
=> 5 × 4928
=> 24640