Question

A circular hole is filled with concrete to make a footing for a load-bearing pier. The hole measures $17$ inches across and requires$1.6$ bags of concrete in order to fill it to ground level. What is the depth of the hole? Round your answer to the nearest inch. (One bag of concrete, when mixed with the appropriate amount of water, makes $1800{in.}^3$ of material).

• A. $17$ in.
• B. $10$ in.
• C. $19$ in.
• D. $13$ in.

Answer 1

Answer: (D)

$13$ in.

Solution;

Let $r$ be the radius of the circle or radius of the top of the cylinder.

$h$ be the height of the cylinder or the depth of the hole.

Given that:

Volume of the one bag concrete and water mixture $=1800i{n}^3$

Diameter of the circle $=17in.$

To find:

The depth of the hole $h=?$

Solution:

Radius of the circle $r=\frac{d}{2}=\frac{17}{2}=8.5in.$

Volume of $1.6$ bags concrete and water mixture $=1.6\times 1800i{n}^3=2880i{n}^3$

Volume of the cylinder filled by concrete and water mixture $\pi r^{2}h$

or, $2880i{n}^3=\pi \times (8.5in{)}^2\times h$

or, $h=\frac{2880i{n}^3}{3.14\times (8.5in{)}^2}$

or, $h=12.68in\approx 13in$

Hence, D is the correct answer.