Question

a cylindrical basin is 2 feet tall and has a diameter of 5 feet, as shown. if the basin is completely filled with water, how much water will it hold? round the answer to the nearest tenth of a foot. \boxed{} ft³

Explanation:

Step1: Find the radius of the cylinder

The diameter is 5 feet, so the radius \( r = \frac{5}{2}= 2.5 \) feet.

Step2: Recall the formula for the volume of a cylinder

The volume \( V \) of a cylinder is given by \( V=\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. Here, \( h = 2 \) feet.

Step3: Substitute the values into the formula

Substitute \( r = 2.5 \) and \( h = 2 \) into the formula: \( V=\pi\times(2.5)^{2}\times2 \).
First, calculate \( (2.5)^{2}=6.25 \). Then, \( V=\pi\times6.25\times2= 12.5\pi \).
Using \( \pi\approx3.14159 \), we get \( V\approx12.5\times3.14159 = 39.269875 \).

Step4: Round to the nearest tenth

Rounding \( 39.269875 \) to the nearest tenth gives \( 39.3 \).

Answer:

\( 39.3 \)