Chapter 12.8, Problem 30STP

To determine

To find: the missing measure in the two similar solids.

Answer to Problem 30STP

Hence,the missing measureis $25cm$ .

Explanation of Solution

Given:

  

  $16cm$

  $25cm$

  $30cm$

  $35cm$

Calculation:

In the first cylinder the height of the cylinder is $20cm$ and the radius of the cylinder is $4cm$ .

In the second cylinder the height of the cylinder is $x$ and the radius of the cylinder is $5cm$ .

Consider the two cylinders are similar.

The objective is to find the value of $x$ .

To find the value of $x$ use the property that two solid figures are similar if they have the same shape and their corresponding linear measurements are proportional.

Since the two cylinders are similar, so the corresponding linear measurements are proportional.

Thus,

  $\begin{array}{l}\frac{20}{x}=\frac{4}{5}\\ 20.5=4x\left[Crossmultiply\right]\\ 100=4x\\ 4x=100\\ x=\frac{100}{4}\left[Dividebothsidesby4\right]\\ =25\end{array}$

Therefore, the value of missing term $x$ is $25cm$ .

Conclusion:

Hence, the missing measure is $25cm$ .