Question

A circular hall(big room) has a hemispherical roof.The greatest height is equal to the inner diameter.Find the area of the floor,given that the capacity of the hall is 48510 cubic meter

Answer 1

let the inner diameter = D
          inner radius = D/2 = r 
Greatest height = D
height of cylindrical part (h)= D-r = r
radius of cylindrical part = r
area of floor = πr²

volume = volume of cylindrical part + volume of hemispherical part
           = πr²h + 2/3 πr³
           = πr³ + 2/3 πr³

⇒$48510= \frac{5}{3} \pi r^{3}$

⇒  $r= \sqrt[3]{ \frac{48510*3}{5 \pi } } = \sqrt[3]{9269.43} =21m$

$Area\ of\ floor= \pi r^{2} = \pi *21^{2}=1386\ m^{2}$

Answer 2

Step-by-step explanation:

here is ur answer

with step by step

is it understandable

area of floor = 1386m²