Chapter 9, Problem 3E

To determine

To find: The amount of concrete needed to make the top of the table.

Answer to Problem 3E

The amount of concrete needed to make the top of the table is $14\text{cubic}\text{feet}$ .

Explanation of Solution

Given information:

The table top is circular with diameter $6\text{feet}$ and depth $\text{6}\text{inches}$ .

Calculation:

Calculate the radius of circular with diameter $6\text{feet}$ and height in feet.

  $\begin{array}{c}r=\frac{d}{2}\\ =\frac{6}{2}\\ =3\text{feet}\end{array}$

  $\begin{array}{c}h=6\text{inches}\\ =\frac{6}{12}\text{feet}\\ =\frac{1}{2}\text{feet}\end{array}$

Using the formulafor volume of cylinder.

  $\begin{array}{c}V=\pi r^{2}h\\ =\pi \times {\left(3\right)}^2\times \frac{1}{2}\\ =\frac{9\pi }{2}\\ =14\cdot 13716694\end{array}$

Rounding to the nearest cubic foot.

  $V=14\text{cubic}\text{feet}$

Therefore, the amount of concrete needed to make the top of the table is $14\text{cubic}\text{feet}$ .