(2) Area of the curved surface
= perimeter of the base u height
= 2 πrh
(3) Area of the whole surface
=(πr^2 2 πrhπr^2 ) = 2 πr(rh)
(4) The volume = area of the base u height
=πr^2 h
Example 3. If the height of a right circular cylinder is 10 cm. and radius of the base
is 7 cm, determine its volume and the area of the whole surface.
Solution : Let, the height of the right circular cylinder is h 10 cm. and radius of
the base is r.
? Its volume =πr^2 h = 3 1416 u 72 u 10
= 1539 38 cube cm. (approx.)
And the area of the whole surface = 2 πr(rh)
= 2 u 3 1416 u 7 ( 7 10 ) sq. cm. (approx.)
= 747 7 sq. cm. (approx.)
Activity : Make a right circular cylinder using a rectangular paper. Determine the
area of its whole surface and the volume.
Example 4. The outer measurements of a box with its top are 10 cm., 9 cm. and
7cm. respectively and the area of the whole inner surface is 262 cm^2. Find the
thickness of its wall if it is uniform on all sides.
Solution : Let, the thickness of the box is x cm.
The outer measurements of the box with top are 10 cm., 9 cm. and 7 cm.
respectively.
? The inside measurement of the box are respectively a ( 10 2 x)cm.,
b ( 9 2 x)cm. and c ( 7 2 x) cm.
? The area of the whole surface of the inner side of the box = 2 (abbcca)
As per question, 2 (abbcca) = 262
or,( 10 2 x)( 9 2 x)( 9 2 x)( 7 2 x)( 7 2 x)( 10 2 x) 131
or, 90 38 x 4 x^2 63 32 x 4 x^2 70 34 x 4 x^2 131 0
or, 12 x^2 104 x 92 0
or, 3 x^2 26 x 23 0
or, 3 x^2 3 x 23 x 23 0
or, 3 x(x 1 ) 23 (x 1 ) 0
or,(x 1 )( 3 x 23 ) 0
or,x 1 0 or, 3 x 23 0
or,x 1 or, 7 67
3
23
x (approx.)