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Question
A metal container in the form of a cylinder is surmounted by a hemisphere of the same radius. The internal height of the cylinder is 7 m and the internal radius is 3.5 m.
Calculate:
- the total area of the internal surface, excluding the base;
- the internal volume of the container in m3.
Solution
Radius of the cylinder = 3.5 m
Height = 7 m
i. Total surface area of container excluding the base = Curved surface area of the cylinder + Area of hemisphere
= `2pirh + 2pir^2`
= `(2 xx 22/7 xx 3.5 xx 7) + (2 xx 22/7 xx 3.5 xx 3.5)`
= 154 + 77 m2
= 231 m2
ii. Volume of the container = `pir^2h + 2/3pir^3`
= `(22/7 xx 3.5 xx 3.5 xx 7) + (2/3 xx 22/7 xx 3.5 xx 3.5 xx 3.5)`
= `539/2 + 539/6`
= `(1617 + 539)/6`
= `2156/6`
= 359.33 m3
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