This is a free lesson from our course in Algebra II Here you'll learn with the help of some examples and practice questions with solution, using video explanation and in own handwriting by the instructor about surface area of above common solids. Any solid formed by joining the corresponding vertices of two congruent and parallel polygons with line segments is known as a prism.The base of a prism is two congruent polygons; lines connecting the corresponding vertices are lateral edges and they are parallel. The parallelograms formed by lateral edges are called lateral faces. (More text below video...)
Other useful lessons:
 Volume - Prisms, Cylinders, Cones, Pyramids and Spheres Effect of dimension changes on volume
(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 = 2 rh + 2 r2
If a cylinder is closed at one end, then
Total surface area of a cylinder = 2 rh + 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 24 cm2.

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.

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