Answer to Question #277276 in Geometry for Mel

Question #277276

A copper hot -water tank is in the form of a cylinder with a hemispherical cap and stands on a flat base . The internal diameter of the cylinder is 525 mm and the overall internal height is 1200 mm .

Calculate : (a) the volume of the tank in m ^ 3 (b) the capacity of the tank in litres


1
Expert's answer
2021-12-09T10:14:52-0500
Rcyl=Rhemisphere=R=5252mm=0.2625mR_{cyl}=R_{hemisphere}=R=\dfrac{525}{2}mm=0.2625m

Hcyl=1.2mR=1.2m0.2625m=0.9375mH_{cyl}=1.2m-R=1.2m-0.2625m=0.9375m

Vcyl=πR2HcylV_{cyl}=\pi R^2H_{cyl}

Vhemisphere=12(4π3R3)V_{hemisphere}=\dfrac{1}{2}(\dfrac{4\pi}{3}R^3)

Vtank=Vcyl+VhemisphereV_{tank}=V_{cyl}+V_{hemisphere}

Vtank=πR2Hcyl+2π3R3V_{tank}=\pi R^2H_{cyl}+\dfrac{2\pi}{3}R^3

=πR23(3Hcyl+2R)=\dfrac{\pi R^2}{3}(3H_{cyl}+2R)

(a)

Vtank=π(0.2625m)23(3(0.9375m)+2(0.2625m))V_{tank}=\dfrac{\pi (0.2625m)^2}{3}(3(0.9375m)+2(0.2625m))

0.240828848 m3\approx0.240828848\ m^3

The volume of the tank is 0.2408288480.240828848 m3.


(b)

The capacity of the tank is 240.829240.829 litres.


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