Question

A buoy consist of a frustum of cone radii 1.0 m 1.8m respectivly height 2.0m to which it is att ached at the larger end of hemisphere of radius 1.8m calculate it volume

Answer 1

Answer:

R = 1.8     r = 1      R - r = .8

h = 2

h / (R - r)  = slope of side of frustum

Let H be height of cone from which frustum  was taken then

H / R = h / (R - r)

H = 2 * 1.8 / .8 = 4.5

Volume of cone of height H:  V = pi R^2 H / 3

V = pi * 1.8^2 * 4.5 / 3 = 15.3 m^3

Volume of cone above frustum

v = pi * r^2 * (H - h) / 3

v = pi * 1 * 2.5 / 3 = 2.62

Thus Vf = 15.3 - 2.62 = 12.7     volume of frustum

Volume of hemisphere = 1/2 * 4 * pi * 1.8^3 / 3 = 12.2 m^3 = Vh

Total volume = Vf + Vh = 12.7 + 12.2 = 24.9 m^3