Question

A well of diameter 13 ft and depth 35 ft is half filled with water. Find the volume of water inside the well.

Answer 1

Hint: A well has the shape of a cylinder. The well is half filled with water. We have to find the volume of water. The shape that the water has assumed inside the well is also a cylinder. The height of the cylinder of water inside the well is half of the height of the well. We will use the formula for the volume of the cylinder to find the volume of water inside the well.

 Complete step by step answer:
The shape of a well is a cylinder. The diameter of this cylinder is given to be 13 ft, so the radius will be half of the diameter, that is 6.5 ft. We have to find the volume of the water inside the well and we know that the well is half filled. The height of the well is given to be 35 ft. So, the water is filled in the well upto half of the height of the well, that is 17.5 ft. To find the volume of water, we will use the formula for the volume of a cylinder.
The volume of a cylinder is given by,
$V=\pi {{r}^{2}}h$
where $r$ is the radius of the cylinder and $h$ is the height of the cylinder. Since the water forms the shape of a cylinder inside the well, we will take the values of radius and height as follows, $r=6.5\text{ ft}$ and $h=17.5\text{ ft}$. Substituting these values in the formula for volume of the cylinder, we get
$V=3.14\times {{\left( 6.5 \right)}^{2}}\times \left( 17.5 \right)$
Simplifying the above equation, we get
$\begin{align}
  & V=3.14\times 42.25\times 17.5 \\
 & =2321.6375\text{ f}{{\text{t}}^{3}}
\end{align}$
Therefore, the volume of the water inside the well is 2321.6375 cubic ft.

Note:
Calculating the volume of the well in this question is not needed. We need to be careful with the given information, it is possible that we mistakenly substitute the value of the diameter in the calculations directly instead of the radius. The calculations need to be done carefully since decimals are involved.