(Continued from above)
In right prism, lateral edges are perpendicular to the bases of the prism and in oblique prism;
lateral edges are not perpendicular to the bases of the prism.
The prism surface area formula is:
2(lw + wh
+ hl)
where l is length, w is width and h is height of the
prism.
E.g. to find the surface area of a rectangular prism 5 cm long, 3 cm wide and 2
cm high, substitute 5 for l, 3 for w and 2 for h in the
above formula i.e. 2(5 x 3 + 3 x 2 + 2 x 5) which works out to 62cm2.
A right circular cylinder is a solid, generated by the revolution of a rectangle
about one of its sides which remain fixed. The curved surface area of a cylinder
with radius r and height h is given by:
Curved surface area
of a cylinder = 2 rh
Total surface area
of a cylinder = 2rh
+ 2r2
If a cylinder is closed at one end, then
Total surface area
of a cylinder = 2rh
+
r2
E.g. to find the surface area of a closed right cylinder with radius 7 m and
height is 10 m, substitute 7 for r and 10 for h in the above formula
i.e. 2 x
x 7 x 10 + 2 x
x 72,
which gives 238
m2.
A right circular cone is a solid generated by the revolution of a right triangle about one of its legs. Slant height of a
right circular cone is the distance from any point on the perimeter of the circular
base to the vertex of the cone.
Slant height = l
=  (r2
+ h2)
Area of curved surface
= rl
Total surface area
of a cone =rl
+ r2
E.g. to find the surface area of a cone, with radius of 7 cm and height is 4 cm,
first you have to find the slant height i.e. l = (32
+ 42) = 5. Now substitute the value of r and l
in the above formula i.e. x
3 x 5 + x
32, which gives 24cm2.
A pyramid is a 3-dimensional figure, whose base is a polygon and triangular lateral
faces that meet at vertex. E.g. pyramids that have a square base, have a total of
five surfaces.
Surface area of a
pyramid = Area of the base + Area of lateral faces
E.g.: to find the surface area of a square pyramid of base 20 m and slant height
40 m, the area of the base which in this case is a square = 202 i.e.
400 and area of lateral faces which is a triangle is = 1/2 x 20 x 40 i.e.
400. Therefore,
Surface area of the
pyramid = 400 + 4(400) = 2000 m2.
|
