Chapter 1.1, Problem 54E

To determine

To find the height of the given solid.

Answer to Problem 54E

  $9\text{ cm}$

Explanation of Solution

Given:

  

Formula used:

Volume of a cuboid:

  $V=l\times b\times h$

Area of rectangle:

  $A=l\times b$

Calculation:

The given image is a cuboid. The base of the cuboid is a rectangle.

From the given image,

Volume $=1323{\text{ cm}}^3$

Area of the rectangle $=l\times b$

  $=147{\text{ cm}}^2$

Volume of cuboid $=l\times b\times h$ where $l\times b$ is the area of rectangle.

Thus,

Volume of cuboid $=\text{Area of the rectangle}\times h$

Substitute the known values in formula (volume of the cuboid).

  $\begin{array}{l}\Rightarrow V=A\times h\\ \Rightarrow 1323=147\times h\\ \Rightarrow h=9\end{array}$

Conclusion:

Therefore, the height of the given solid is $9\text{ cm}.$