 Hello and welcome to the session. Let us discuss the following question. It says, a dome of a building is in the form of a hemisphere. From inside it was whitewashed at the cost of rupees 498.96. If the cost of whitewashing is rupees 2 per square meter, find the inside surface area of dome volume of the air inside the dome. Let us first do the formula for volume of the hemisphere because dome is in the form of hemisphere. This formula is 2 by 3 pi r cube where r is the radius and value of pi is 22 upon 7. Let us now move on to the solution. In the first part we have to find the surface area of the dome. Now we are given that the total cost of whitewashing is rupees 498.96 and the cost of whitewashing per square meter area is rupees 2. Now the total cost of whitewashing is equal to this area of dome. Washing implies the curve surface area or the surface area of dome is equal to the total cost upon the cost of whitewashing per square meter. Now the total cost is rupees 498.96 and the cost of whitewashing per square meter area is rupees 2. So the area is 249.48 meter square. Now in the second part we have to find volume of the air inside the dome. That means we have to find the volume of the hemispherical dome and its formula is 2 by 3 pi r cube. So we need to find r that is the radius of the hemispherical dome. From the first part we know that the curve surface area of dome is equal to 249.48 meter square. And we know that the curve surface area hemispherical is 2 pi r square. Since the dome is in the form of hemisphere the surface area of dome is equal to 2 pi r square which is equal to 249.48 meter square. So this implies 2 pi r square is equal to 249.48 meter square. And this implies r square is equal to 249.48 upon 2 pi meter. And this implies r square is equal to 249.48 upon 2 into pi which is 22 upon 7. That is is equal to 249.48 into 7 upon 44 which is equal to 39.69 meter. So this implies r is equal to under the root of 39.69 meter which is equal to 6.3 meter. Now we find the volume of the dome by 3 pi r cube. Now r is 6.3 meter. So substituting the values of pi and r in the formula we have 2 by 3 into 22 by 7 into 6.3 cube and the unit of volume is meter cube which is again equal to 2 by 3 into 22 by 7 into 6.3 into 6.3 into 6.3 and simplifying this we get the volume as 223.9 meter cube approximately. Hence the surface area of the dome is 249.48 meter square and the volume of the air inside the dome is 523.9 meter cube approximately. So this completes the question. Bye for now. Take care. Have a good day.