Question

A well of diameter 150 cm has a stone parapet around it. If the length of the outer edge of the parapet is 660cm then find the width of the parapet.

Answer 1

Hint: As we know that a well is a cylinder in shape.
 A cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line.

Complete answer:

Given, the Diameter of the well \[\left( d \right) = {\text{15}}0cm.\]
Therefore the radius of well =\[75cm\]
Let the radius and diameter of the parapet is r and D respectively.
Since, length of the outer edge of the parapet =\[660cm\]
Therefore,
⇒\[{\text{2}}\pi r = {\text{66}}0cm\]
⇒\[2r = \dfrac{{{\text{66}}0}}{\pi }\]
⇒\[{\text{2}}r = \dfrac{{{\text{66}}0 \times {\text{7}}}}{{22}}\]
⇒\[r = {\text{1}}05cm\]
Therefore, \[r = {\text{1}}0{\text{5}}cm\], \[{\text{D = 210 cm}}\]

Now, width of the parapet = (Radius of parapet – Radius of the well) \[ = ({\text{1}}0{\text{5}} - {\text{75}}) = {\text{3}}0cm\]
Hence, width of the parapet is \[{\text{3}}0\;cm\]

Note: Parapet is also known as embankment. Parapets were originally used to defend buildings from military attack, but today they are primarily used as guard rails and to prevent the spread of fires. In the Bible, the Hebrews are obligated to build a parapet on the roof of their houses to prevent people from falling.