Question

A dome of building in the form of a hemisphere. From inside it was white washed at the cost of Rs. 4989.60.If the cost of white washing is Rs. 20 per square meter.Find the Inside Surface of the dome​

Answer 1

Answer:

Good morning.. Hi there.. Here's the answer for your question..

Step-by-step explanation:

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

Hope it helps you..

If any doubt ask me..

Thank you..