Chapter 12.8, Problem 3CYU

To determine

To find: the missing measure for each pair of similar solids.

Answer to Problem 3CYU

The value of missing term d is 4.

Explanation of Solution

Given:

  

Calculation:

In the first cylinder the height of the cylinder is 2 yd and the diameter of the cylinder is d yd.

In the second cylinder the height of the cylinder is 6 yd and the diameter of the cylinder is 12 yd.

Consider the two cylinders are similar.

The objective is to find the value of d.

To find the value of d 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,

  $\begin{array}{l}\frac{d}{12}=\frac{2}{6}\\ d\cdot 6=2\cdot 12\text{ [Cross Multiply]}\\ 6d=24\\ d=\frac{24}{6}\text{ [Divide both sides by 6]}\\ =4\end{array}$

Conclusion:

Therefore, the value of missing term d is 4.