Question A satellite is to be constructed in the shape of a cylinder with a hemisphere at

Question

Transcribed Image Text:

A satellite is to be constructed in the shape of a cylinder with a hemisphere at each end. The radius of the cylinder is r metres and its height is h metres (see diagram below). The outer surface area of the satellite is to be coated with heat-resistant material which is very expensive. The volume of the satellite has to be cubic metres. 6 10.1 10.2 10.3 D Show that h= 6r 61-² 3 h Outer surface area of a sphere = 4.7² Curved surface area of a cylinder = 2.7rh 4 Volume of a sphere ar 3 Volume of a cylinder = r²h Hence, show that the outer surface area of the satellite can be given as 47r² 7 S= 3 3r Calculate the minimum outer surface area of the satellite. A satellite is to be constructed in the shape of a cylinder with a hemisphere at each end. The radius of the cylinder is r metres and its height is h metres (see diagram below). The outer surface area of the satellite is to be coated with heat-resistant material which is very expensive. The volume of the satellite has to be cubic metres. 6 10.1 10.2 10.3 D Show that h= 6r 61-² 3 h Outer surface area of a sphere = 4.7² Curved surface area of a cylinder = 2.7rh 4 Volume of a sphere ar 3 Volume of a cylinder = r²h Hence, show that the outer surface area of the satellite can be given as 47r² 7 S= 3 3r Calculate the minimum outer surface area of the satellite.