Chapter 6.5, Problem 4CYP

To determine

To find:thedimensions of the both cubes.

Answer to Problem 4CYP

  $5cm\text{ and }15cm$ .

Explanation of Solution

Given:

The volume of the objectis $32550c{m}^3$ .

Length of the smaller cube is one-third of the length of the larger cube.

Calculation:

According to the question, length of the smaller cube is one-third of the length of the larger cube.

Let x be length of the smaller cube,

Therefore, length of the larger cube is $3x$ .

As the volume of the object is the difference between the cubes, therefore,

  $\begin{array}{l}{\left(3x\right)}^3-x^3=3250\left\{\text{volume of the object}\right\}\\ 27x^3-x^3=3250\left\{\text{simplify}\right\}\\ 26x^3=3250\left\{\text{subtract like terms}\right\}\\ x^3=\frac{3250}{26}\left\{\text{divide both sides by 26}\right\}\\ x^3=125\\ x=\sqrt[3]{125}=5\left\{\text{taking cube roots on both sides}\right\}\end{array}$

Thus, the length of smaller cube is $x=5cm$

And, the length of larger cube is $3x=3\times 5=15cm$

Hence,the dimensions of the both cubes are $5cm\text{ and }15cm$ .