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:

1. the total area of the internal surface, excluding the base;
2. the internal volume of the container in m³.

Answer 1

 
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