a building is in the form of a right circular cylinder surmounted by a hemisphere both having same radii - Maths -

Question

a building is in the form of a right circular cylinder
surmounted by a hemisphere both having same radii the base
diameter= 2/3 of total height of the building find the height of
the building if it contains 67 1/21 m3 AIR

Mohil · Answer

Let h be the height of cylinder and r be the common base radii of cylinder and hemisphere and H be total height of building

Diameter of dome = 2r $n n \Rightarrow n Diameter of dome n n n = n \frac{n}{n 2 n} n n n â¢ n n \times n â¢ n n Total height of building n â¢ n n n n \Rightarrow n 2 n r n = n \frac{n}{n 2 n} n â¢ n n \times n â¢ n H n n n n 2 n r n = n \frac{n}{n 2 n} n n (n h n n n + n n n r n n n n n) n n n n n n n$ 6r = 2h + 2r 4r = 2h ⇒h = 2r According to given condition, Volume of air inside the building = Volume of cylinder + Volume of hemisphere $n n \frac{n}{n 1408 n} n = n π n n^{n r n n n 2 n n} n h n + n \frac{n}{n 2 n} n π n n^{n r n n n 3 n n} n n n n \frac{n}{n 1408 n} n = n π n n^{n r n n n 2 n n} n n n [n h n + n \frac{n}{n 2 n} n r n] n n n n n = n π n n^{n r n n n 2 n n} n n n [n 2 n r n + n \frac{n}{n 2 n} n r n] n n n n n = n π n n^{n r n n n 2 n n} n n n [n \frac{n}{n 6 n r n + n 2 n r n} n] n n n n n \frac{n}{n 1408 n} n = n \frac{n}{n π n} n n^{n r n n n 2 n n} n n (n 8 n r n) n n n n n \Rightarrow n \frac{n}{n 1408 n} n = n 8 n n^{n r n n n 3 n n} n n n n \frac{n}{n 1408 n} n = n 8 n n^{n r n n n 3 n n} n n n n \Rightarrow n n^{n r n n n 3 n n} n = n \frac{n}{n 1408 n} n n n n \Rightarrow n n^{n r n n n 3 n n} n = n \frac{n}{n 176 n} n = n 8 n n n n n n n n n n n n n n n n n n n n n$ r 3 = 8 ⇒ r 3 = (2)3 ⇒ r = 2 cm ∴ h = 2r = 2 × 2 = 4 cm Hence height of building = H = h + r = 4 + 2 = 6 cm

a building is in the form of a right circular cylinder surmounted by a hemisphere both having same radii. the base diameter= 2/3 of total height of the building. find the height of the building if it contains 67 1/21 m3 AIR

a building is in the form of a right circular cylinder surmounted by a hemisphere both having same radii. the base diameter= 2/3 of total height of the building. find the height of the building if it contains 67 1/21 m³AIR