Question

a circular hall has a hemispherical roof. the greatest height is equal to the inner diameter. find the radius given that the total volume is 48510m^3. [ans. is 21m} please show working.

Answer 1

Answer:

21 m

Step-by-step explanation:

Let the radius be 'r'.

∴ Volume of the cylindrical portion = πr² * r = πr³

∴ Volume of hemispherical portion = (2/3) πr³ m³.

∴ Volume of air in the hall = (πr³ + 2/3 πr³)

                                           = (5/3) πr³ m³

Now,

⇒ (5/3) πr³ = 48510

⇒ (5/3) * (22/7) * r³ = 48510

⇒ (110) r³ = 48510 * 21

⇒ 110 * r³ = 1018710

⇒ r³ = 1018710/110

⇒ r³ = 9261

⇒ r = 21m.

Therefore, radius = 21 m.

Hope it helps!

Answer 2

Answer:

~21

Step-by-step explanation:

let radius of the hall = r

As per question= Volume of cylindrical Hall + Volume of dome

                       = πr²*r+ (4/3) πr³/2

                       = πr³ + 2πr³/3 =5πr³/3

then we have    5πr³/3=48510

                             r³=9264.72

                        ⇒  r=21.0028