Question

A dome ot's building is in the form of a Hemispulil.
at the cost of 4989.60. If the cost of white-washing is 20 per square metre, found the
(1) inside surface area of the dome,
(2) volume of the air inside the dome,


Don't Spam plz
Only give Correct Answer
​

Answer 1

Answer:We know that Area white washed×Cost of white wash=Total cost

Area white washed×20=4989.60

Area white washed =  

20

4989.60

​  

=249.48‬‬m  

2

 

Now, area white washed is curved surface area of hemisphere(as only walls are whitewashed, not floor)

∴,inner surface area of dome =249.48‬‬m  

2

 

Volume of air inside dome=volume of hemisphere=  

3

2

​  

πr  

3

 

Let the radius of dome be rm

Let us first find the radius using surface area

Surface area of dome=249.48‬‬m  

2

 

⇒2πr  

2

=249.48‬‬m  

2

 

⇒2×  

7

22

​  

×r  

2

=249.48‬‬m  

2

 

⇒r  

2

=  

2×22

249.48‬‬×7

​  

=39.69‬

⇒r=  

39.69‬

​  

=6.3m

Volume of the air inside the dome=Volume of hemisphere

=  

3

2

​  

πr  

3

 

=  

3

2

​  

×  

7

22

​  

×6.3‬×6.3×6.3m  

3

=523.908m  

3

Step-by-step explanation:

Answer 2

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