the sum of the radius and height of a cylinder is 37cm and total surface area of the cylinder is 1628 cms . Find the height and the volume of the cylinder
Answers
Let r and h are the radius and height of the cylinder respectively
Sum of radius and height = 37
r + h = 37 cm
Total surface area of cylinder = 1628 sq.cm
2 Π r (h + r) = 1628
2 Π r (37) = 1628
2 Π r = 1628/37
2 Π r = 44
2 x (22/7) x r = 44
r = 44 x (1/2) x (7/22)
r = 7
7 + h = 37
h = 37 - 7
h = 30 cm
Volume of the right circular cylinder = Π r² h
= (22/7) x (7)² x (30)
= (22/7) x (7) x (7) x (30)
= (22) x (7) x (30)
= 4620 cm³
Volume of cylinder = 4620 cm³
Height = h m
Given (r+h)=37m
Total surface area= 2*pi*r(r+h)=1628
2*22/7* r*37=1628
r=(1628*7)/(2×22×37)
After cancellation
r=7 m
r+h =37
7+h=37
h=30m
i) csa of the cylinder=2*pi*r*h
=2*22/7*7*30
=1320 m^2
Voume =pi*r^2*h
=22/7*7*7*30
=4620m^3