Chapter 12.6, Problem 21HP

To determine

Calculate the surface area of ice cubes and state faster melting of either of them

  

Answer to Problem 21HP

Ice cube having half cylindrical shape will melt rapidly than rectangular ice cube.

Explanation of Solution

Given:

  

Calculations:

Here, we have to calculate surface area of rectangular prism and half cylindrical prism

We know that, surface area of rectangular prism is calculated as,

  $\begin{array}{l}Surfacearea=2(width\times length)+2(length\times height)\\ =2(2.5\times 3)+2(3\times 3)\\ =15+18\\ =33c{m}^2\end{array}$

We know that, surface area of half cylinder is calculated as,

  $Surfacearea=\pi r^2+\pi rh$

Where, r is the radius of cylinder h is the height of cylinder

Putting values in equation, we get

  $\begin{array}{l}\left(Surfacearea\right)=\pi r^2+\pi rh\\ =(3.14\times {1.7}^2)+(3.14\times 1.7\times 5)\\ =9.0746+26.69\\ \left(Surfacearea\right)=35.764c{m}^2\end{array}$

We know that, ice cubes with larger surface area melts faster. Thus, ice cube having half cylindrical shape will melt rapidly than rectangular ice cube.

Conclusion:

Therefore, we are able to calculate surface area of given ice cubes using simple formula.