A storage tank is in the shape of a frustum surmounted by a cone. The frustum of cone has base diameters 4m and 6m respectively. The frustum is standing on a base of diameter 4m and on the other base there is a cone of the same diameter and of height 7m. If the entire height of the storage tank is 10.5m, find the capacity of the storage tank.
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Answer:
Total Volume = 69.6 + 66 = 135.6 cubic meter.
Step-by-step explanation:
The tank is in the shape of attached picture.
The total height = 10.5m
Height of top cone = 7m
Height of frustum = 10.5 – 7 = 3.5m = h.
Big radius of frustum = 6/2 = 3m = R
Small radius of frustum = 4/2 = 2m. = r
Volume of frustum = V = πh (R^2+rR+r^2)/3
= 22*3.5*(3*3 + 3*2 + 2*2)/(3*7)
= 69.6 cubic meter.
Radius of base of cone = 6/2 = 3m
Height of Cone = 7m
Volume of cone = πhr^2/3 = 22*3*3*7/(3*7)
= 66 Cubic meter.
Total Volume = 69.6 + 66 = 135.6 cubic meter.
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