Question

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome which contains 17.7 m cube of air and its internal diameter is equal to the height of the crown of the vault above the floor .find the height of the building (Take π =22\7)

Answer 1

this is a solution of your answer

Answer 2

The correct answer is 3.002 m.

Given: Volume = 17.7 $m^{3}$.

Internal diameter = height.

To Find: Height of the building.

Solution:

Let the radius of cylinder = r

Height of building = h

As given in question, h = 2r.

Radius of hemisphere = r.

Volume of dome = $\pi r^{2}*r +\frac{2}{3} \pi r^{3}$

= $\pi r^{3} +\frac{2}{3} \pi r^{3}$

= $\pi r^{3} (1+\frac{2}{3} )$

= $\frac{5\pi r^{3} }{3}$

Now as given that volume = 17.7 $m^{3}$.

$\frac{5\pi r^{3} }{3}=17.7$

$\frac{5*22*r^{3} }{3*7} =17.7$

$r^{3} =\frac{17.7*3*7}{5*22}$

$r^{3} =3.38$

r = 1.501 m

Height = 2r = 2*1.501 = 3.002 m.

Hence, the height of the dome is 3.002 m.

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