Surface Area Of A Solid Right Circular Cyllinder
Introduction to surface area a right circular cylinder :
The surface area of right circular cylinder is the the area of all the parts needed to cover the right circular cylinder.
Radius of a right circular cylinder : The radius of any circular cross-section is called the radius of the right circular cylinder.
Height of a right circular cylinder : The distance between the centres of circular cross-sections at the ends is called the height (or length) of the cylinder.
Surface Area of a Solid Right Circular Cyllinder
Let r be the radius and h be the height of a solid cylinder, then
(i) Curved (lateral) surface area
= Perimeter of cross-section X Height
= 2'pi'rh.
(ii) Total surface area
= Curved surface area + Area of two circular ends
= 2'pi'rh + 2 'pi'r2
= 2'pi'r( h + r).
(iii) Volume =Area of cross-section X Height
= 'pi'r2h.
Surface Area of a Hollow Right Circular Cyllinder
Let R and r be the external and internal radii of a hollow cylinder, and h be its height, then
(i) Thickness of right circular cylinder
= R - r.
(ii) Area of cross-section = 'pi'(R2- r2).
(iii)External curved surface area = 2'pi'Rh.
(iv) Internal curved surface area = 2 'pi'rh.
(v) Total surface area = External curved surface area + Internal curved surface area + Area of two ends.
= 2'pi'Rh + 2 'pi'rh +2'pi'(R2- r2)
= 2 'pi'(Rh + rh + R2- r2 ).
(vi) Volume of the material ='pi'R2h - 'pi'r2h
= 'pi'( R2 - r2)h.
Problem on Surface Area of Right Circular Cyllinder
Problem 1.
Determine the curved surface area of a right circular cylinder with a base of radius 5 inches and a height 14 inches.
Solution :
Curved surface area = 2'pi'rh
= 2 X 5 X 14 sq.inches. [ Since, r = 5 inches, h = 14 inches,'pi' = 3.14 ]
=140 sq.inch. ( Answer)
Problem 2.
Determine the total surface area of a right circular cylinder with a base of radius 4cm. and height 8cm.
Solution :
Total surface area = 2'pi'r(h + r).
= 2 X 3.14 X 4cm( 8 +4 )cm.
= 301.44 sq.cm. (Answer)
Problem 3.
The volume of a right circular cylinder is 616 cm3 and its height is 16 cm.
Find the radius and the total surface area.
Solution :
Let r cm be the radius of the circular cylinder, then its
volume = 'pi'r2 h = 616 cm3 (given)
'rArr' 22/7 X r2 X 16 = 616
'rArr' r2 = 616 X 7 / 22 X 16
'rArr' r2 = 49/4
'rArr' r = 7/2 = 3.5
So, Radius of cylinder = 3.5 cm. (Answer)
Total surface area = 2'pi'r (h + r)
= 2 X 22/7 X 7/2(16 + 7/2) cm2
= 429 cm2 . (Answer)
by: jeri
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