Answer to Question #277276 in Geometry for Mel

Question

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

Answer 1

$$R_{cyl}=R_{hemisphere}=R=\dfrac{525}{2}mm=0.2625m$$

$$H_{cyl}=1.2m-R=1.2m-0.2625m=0.9375m$$

$$V_{cyl}=\pi R^2H_{cyl}$$

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

$$V_{tank}=V_{cyl}+V_{hemisphere}$$

$$V_{tank}=\pi R^2H_{cyl}+\dfrac{2\pi}{3}R^3$$

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

(a)

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

$$\approx0.240828848\ m^3$$

The volume of the tank is $0.240828848$ m³.

(b)

The capacity of the tank is $240.829$ litres.