Question

1. Determine a rule that could be used to explain how the volume of a

Answer 1

Answer:

See explanation

Step-by-step explanation:

Solution:-

- We will use the basic formulas for calculating the volumes of two solid bodies.

- The volume of a cylinder ( V_l ) is represented by:

                                  $V_c = \pi *r^2*h$

- Similarly, the volume of cone ( V_c ) is represented by:

                                  $V_c = \frac{1}{3}*\pi *r^2 * h$

Where,

               r : The radius of cylinder / radius of circular base of the cone

               h : The height of the cylinder / cone

- We will investigate the correlation between the volume of each of the two bodies wit the radius ( r ). We will assume that the height of cylinder/cone as a constant.

- We will represent a proportionality of Volume ( V ) with respect to ( r ):

                                  $V = C*r^2$

Where,

            C: The constant of proportionality

- Hence the proportional relation is expressed as:

                                 V∝ r^2

- The volume ( V ) is proportional to the square of the radius. Now we will see the effect of multiplying the radius ( r ) with a positive number ( a ) on the volume of either of the two bodies:

                                $V = C*(a*r)^2\\\\V = C*a^2*r^2$

- Hence, we see a general rule frm above relation that multiplying the result by square of the multiple ( a^2 ) will give us the equivalent result as multiplying a multiple ( a ) with radius ( r ).

- Hence, the relations for each of the two bodies becomes:

                              $V = (\frac{1}{3} \pi *r^2*h)*a^2$

                                          &

                              $V = ( \pi *r^2*h)*a^2$