Chapter 1.1, Problem 56E

To determine

To find the height of the given solid.

Answer to Problem 56E

  $\frac{7}{6}\text{ ft}$

Explanation of Solution

Given:

  

Formula used:

Volume of a pyramid:

  $V=\frac{l\times w\times h}{3}$

Area of square:

  $A=a^2$

Calculation:

The given image is a pyramid. The base of the pyramid is square. Therefore, the area of the base is the area of the base of the square.

From the given image,

Volume $=35{\text{ ft}}^3$

Base of the pyramid is a square,

B $=30{\text{ ft}}^2$

Therefore, the width of the square and the length of the square are the same.

Area of the square $=a^2$

  $=30{\text{ ft}}^2$

  $\begin{array}{l}\Rightarrow A=a^2\\ \Rightarrow 30=a^2\end{array}$

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

  $\begin{array}{l}\Rightarrow V=l\times w\times h\\ \Rightarrow V=A\times h\\ \Rightarrow 35=30\times h\\ \Rightarrow h=\frac{35}{30}\\ \Rightarrow h=\frac{7}{6}\text{ ft}\end{array}$

Conclusion:

Therefore, the height of the given solid is $\frac{7}{6}\text{ ft}.$