A dome of a building is of the form of a hemisphere . inside of it is white washed at rupees 40. 50 per m^2 .total cost of whitewashing is rupees 12474. Find (i) the number one the inner surface area of a Dome (ii) the volume of air inside the dome.
Answers
Answer:
Step-by-step explanation:
the inner surface area of the dome is nothing but the total cost of whitewashing divided by the rate per metre. hence inner surface area= 498.96 / 2 = 249.48 m^2. now, inner surface area = 2πr^2. therefore 2πr^2 = 249.48, which gives r = 6.3 m. so, volume = 2/3*πr^3 = 523.908 m^3.
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Answer:
(i) 308 m² (ii) 718.67 m³
Step-by-step explanation:
Gn:
Cost of painting 1 m² = Rs. 40.50
Total cost = Rs. 12474
To find:
(i) inner surface area
(ii) volume of air inside
(i)
C.S.A of hemisphere = 2πr²
1 m² = Rs. 40.50
2πr² = 2πr² * 40.50
But, it is given that the cost was Rs. 12474
therefore:
2πr² * 40.50 = 12474
2πr² = 12474 / 40.50
2πr² = 308 m²
therefore the area was 308 m²
(ii)
2πr² = 308
r² = 308 * 7 / 22 * 2
r² = 7²
r = 7
Volume of hemisphere = 2/3πr³
= 2/3 * 22/7 * (7)³
= 718.67 m³
therefore the volume of air in the dome is 718.67 m³