Shankar made the following pictures also.

What shapes can they be broken into, of which we can find area easily ?
Make some more pictures and think of the shapes they can be divided into different parts.

A container shpaed like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice creqa. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

A container, open from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container, at the rate of Rs 20 per litre. also find the cost of metal sheet used to make the container, if it cost Rs 8 per 100 cm^(2) (Take pi=3.14)

A physical quantity is a phyical property of a phenomenon , body, or substance , that can be quantified by measurement. The magnitude of the components of a vector are to be considered dimensionally distinct. For example , rather than an undifferentiated length unit L, we may represent length in the x direction as L_(x) , and so forth. This requirement status ultimately from the requirement that each component of a physically meaningful equation (scaler or vector) must be dimensionally consistent . As as example , suppose we wish to calculate the drift S of a swimmer crossing a river flowing with velocity V_(x) and of widht D and he is swimming in direction perpendicular to the river flow with velocity V_(y) relation to river, assuming no use of directed lengths, the quantities of interest are then V_(x),V_(y) both dimensioned as (L)/(T) , S the drift and D width of river both having dimension L. with these four quantities, we may conclude tha the equation for the drift S may be written : S prop V_(x)^(a)V_(y)^(b)D^(c) Or dimensionally L=((L)/(T))^(a+b)xx(L)^(c) from which we may deduce that a+b+c=1 and a+b=0, which leaves one of these exponents undetermined. If, however, we use directed length dimensions, then V_(x) will be dimensioned as (L_(x))/(T), V_(y) as (L_(y))/(T), S as L_(x)" and " D as L_(y) . The dimensional equation becomes : L_(x)=((L_(x))/(T))^(a) ((L_(y))/(T))^(b)(L_(y))^(c) and we may solve completely as a=1,b=-1 and c=1. The increase in deductive power gained by the use of directed length dimensions is apparent. From the concept of directed dimension what is the formula for a range (R) of a cannon ball when it is fired with vertical velocity component V_(y) and a horizontal velocity component V_(x) , assuming it is fired on a flat surface. [Range also depends upon acceleration due to gravity , g and k is numerical constant]