The surface area of a spherical dome-shaped roof of a cylindrical water tank shown in the figure is

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Q: 142 (IAS/1999)
The surface area of a spherical dome-shaped roof of a cylindrical water tank shown in the figure is

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,1,1,0,1,1,0

keywords: 

{'spherical dome': [0, 1, 0, 0], 'surface area': [0, 2, 1, 0], 'cylindrical water tank': [0, 1, 0, 0], 'roof': [0, 0, 0, 1], 'pi m2': [0, 1, 0, 0], '60pi m2': [0, 1, 0, 0], '300pi m2': [0, 1, 0, 0], '109pi m2': [0, 1, 0, 0]}

The surface area of a spherical dome can be calculated with the formula 2πrh, where r is the radius of the base of the dome and h is the height of the dome.

In the first option, 60π m2 represents a case where 2πrh=60. Given the physical reality of a spherical dome, this would correspond to fairly small values for both r and h.

Option 2 gives a surface area of 109π m2 which means 2πrh=109. This represents a dome that is larger than in option 1.

Option 3 shows a surface area of 120 π m2, meaning 2πrh=120. The dome here is even larger than in option 2.

Lastly, option 4 suggests a surface area of 300π m2 where 2πrh=300. This is the largest dome of all the options.

Given these explanations, without values for r or h we can not definitively say which option is correct. But, if the correct answer given is option 2, it suggests that the value of 2πrh for the given sphere is 109.