Question

volume
a cylindrical water bucket holds 71.6 cubic inches of water to keep it completely full. if the diameter of the base (bottom) is 4.5 inches, how tall must it be? use 3.14 for π and round your answer to the nearest hundredth.

Explanation:

Step1: Identify the shape and formula

The problem is about a cylinder (since it's a water tank, likely a cylinder). The volume formula for a cylinder is \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. Given the diameter is 4.5 inches, the radius \( r=\frac{4.5}{2} = 2.25 \) inches, and the height \( h = 71.6 \) inches. We use \( \pi\approx3.14 \).

Step2: Substitute values into the formula

Substitute \( r = 2.25 \), \( h=71.6 \), and \( \pi = 3.14 \) into the formula:
\( V=3.14\times(2.25)^{2}\times71.6 \)

First, calculate \( (2.25)^{2}=2.25\times2.25 = 5.0625 \)

Then, calculate \( 3.14\times5.0625=15.89625 \)

Then, calculate \( 15.89625\times71.6 \)

\( 15.89625\times71.6 = 15.89625\times(70 + 1.6)=15.89625\times70+15.89625\times1.6 \)

\( 15.89625\times70 = 1112.7375 \)

\( 15.89625\times1.6=25.434 \)

Add them together: \( 1112.7375+25.434 = 1138.1715 \)

Answer:

The volume of the water tank is approximately \( 1138.17 \) cubic inches (rounded to two decimal places) or following the calculation steps, the value is \( 1138.1715 \) cubic inches. If we consider the calculation with more precise steps, the final volume is \( \boldsymbol{1138.17} \) (or as per the required precision) cubic inches.