Question

A rectangular solid (cuboid shape) of wax with diameters 66 cm,42 cm,21 cm is used to prepare 375 cylindrical candles having diameter 2.1 cm ,height 2.8 cm .Is it true? Support your answer.

Answer 1

Hint: Here we have to check if volume of wax is equal to volume of all candles.We know that volume of a cuboid is $length \times width \times height$ and volume of a cylinder is $\pi \times radiu{s^2} \times height$ .

Complete step-by-step answer:

Step1:The volume of the wax is
     $\eqalign{
  & {V_1} = length \times width \times height \cr
  & = 66 \times 42 \times 21 \cr
  & = 58212\,\,c{m^3} \cr} $
Step2: The volume of each candle is
    $\eqalign{
  & = \pi \times radiu{s^2} \times height \cr
  & = \pi \times {\left( {\dfrac{{2.1}}{2}} \right)^2} \times 2.8 \cr
  & = {\text{9}}{\text{.69809652}}\,\,c{m^3} \cr} $
Step3: The volume of 375 candles is
 $\eqalign{
  & {V_2} = 375 \times {\text{9}}{\text{.69809652}} \cr
  & = {\text{3,636}}{\text{.786195}}\,\,c{m^3} \cr} $
Step4:Since .${V_1} \ne {V_2}$. ,it is not true.

Note: The above preparation is only possible if .${V_1}$ = ${V_2}$. That is both volume i.e. volume of wax and volume of 375 candles to be equal.