Chapter 12.8, Problem 19PPS

To determine

The missing measure value of the given pairs of similar solids is to be estimated.

  

Answer to Problem 19PPS

The missing measure value of the given pairs of similar solids is $x=3.33in$ .

Explanation of Solution

Given:

  

  $\begin{array}{l}{V}_1=2250c{m}^3\\ V_2=18c{m}^3\\ L_1=45cm\\ L_2=xcm\end{array}$

Concept Used:

When the pairs of solids are similar the ratio of the dimensions of the solids is same.

The surface area of cylinder is given by the following expression:

  $S=2\pi r\left(h+r\right)$

Where,

Radius of circular portion: $r$

Height of cylinder: $h$

Calculation:

The surface area of large cylinder is given by the following expression:

  $\begin{array}{l}{S}_1=2\pi r_1\left(h_1+r_1\right)\\ 942=2\pi \left(\frac{15}{2}\right)\left(h_1+\left(\frac{15}{2}\right)\right)\\ h_1+\left(\frac{15}{2}\right)=19.9898\\ h_1=12.4898in\end{array}$

Know that:

The given pair of solids is similar, so take the ratio its dimension’s is same. Hence, the missing measure value of $x$ is calculated as:

  $\begin{array}{l}\frac{h_1}{h_2}=\frac{r_1}{r_2}\\ \frac{12.4898}{x}=\frac{\left(\raisebox{1ex}{$15$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}{2}\\ x=\frac{12.4898\times 4}{15}\\ x=3.33in\end{array}$

Conclusion:

Hence, missing measure value of $x$ is calculated as $x=3.33in$ .