water volume

Geometry Level 3

a cylinderical tank is fixed horizontally for water storage as shown on figure , the tank is filled with water up to a maximum depth of 1.50 m. if the volume of water ( in m 3 m^3 ) is a π + b √ 3 3 \frac{aπ + b√3 }{3} , where a and b are positive integers find a + b .


The answer is 22.

Aziz Alasha by Aziz Alasha , 59, Sudan

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1 solution

Tom Engelsman
Sep 6, 2017

The water's cross-sectional area is comprised of a 240-degree circular sector (radius = 1) and a isosceles triangle (base = 3 \sqrt{3} and height = 1 2 \frac{1}{2} ). The entire volume is computed to be:

V = B h = [ 1 2 ( 1 2 ) ( 4 π 3 ) + 1 2 ( 1 2 ) ( 3 ) ] ⋅ 8 = [ 2 π 3 + 3 4 ] ⋅ 8 = 16 π + 6 3 3 . V = Bh = [\frac{1}{2}(1^2)(\frac{4\pi}{3}) + \frac{1}{2}(\frac{1}{2})(\sqrt{3})] \cdot 8 = [\frac{2\pi}{3} + \frac{\sqrt{3}}{4}] \cdot 8 = \boxed{\frac{16\pi + 6\sqrt{3}}{3}}.

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