Solids

Solid means having three dimensions (length, breadth and thickness), as a geometrical body or figure. Or it may also be defined as relating to bodies or figures of three dimensions.

Prism and their surface area and volume

Prisms are the solid object that has two opposite faces congruent and parallel.

The above figures are different solid figures which have congruent opposite face.

Each congruent face of a prism is called its cross-section. There are infinite numbers of imaginary surfaces that cut the prism perpendicular to its height or length with congruent surfaces.

Total surface area of prism

Let's take a cartoon box. While unfolding the cartoon box, there we can find many faces of the boxes. Measure all the surfaces and find the area of each surface. If the length is “l” breadth is “b” and height is ‘h’, what will be the total surface area?

In a box, altogether there are 6 surfaces. Among them three pairs are congruent. Thus, total surface area (A) = 2(l \(\times\) b) + 2(b \(\times\)h) + 2(l \(\times\) h) square units

= 2(lb + bh + lh) square units.

In the case of irregular shape, area of surface are calculated separately and added to find out the total surface area.

Lateral surface area of prism

The sum of areas of four lateral surfaces of the prism is called the lateral surface area of the prism.

Lateral surface area (S) = 2(l \(\times\) h) + 2(b \(\times\) h)

= 2lh + 2bh

= h \(\times\) 2(l+b)

= h \(\times\) p

\(\therefore\) lateral surface area (S) = height \(\times\) perimeter of base

Total surface area of the prism (TSA) = Lateral surface area + 2 \(\times\) area of cross section

i.e. TSA =LSA + 2A

Volume of prism

let's take a cuboidal prism.

For a cuboid	For a cube
Volume (V) = l \(\times\) b \(\times\) h V = A \(\times\) H Where, A = l \(\times\) b	Volume (V) = l \(\times\) l \(\times\) l (V) = l2 \(\times\) l (V) = A \(\times\) l

Thus, Volume = Area of cross-section × height