Question

A square with an area of 100m^2 is rotated around a center line what is the volume of the solid formed

Answer 1

Consider that if a square is rotated about a center line, the 3d solid produced will be a right circular cylinder with the height and diameter of base, both being equal to the side of the side of the square,

Let the side of the square be 'x'.

It is given that the area of the square is 100 sq. meters,

`\begin{gathered} \text{Area}=100 \\ x^2=100 \\ x=10 \end{gathered}`

Thus, the side of the square is 10 meters.

As dscussed above, the diameter (d) and height (h) of the cylinder will be the same as the side of the square,

`\begin{gathered} d=10 \\ h=10 \end{gathered}`

Then the volume of the cylinder is calculated as,

`\begin{gathered} V=(\pi)/(4)d^2h \\ V=(\pi)/(4)(10)^2(10) \\ V=250\pi \\ V\approx785.398 \end{gathered}`

Thus, the volume of the resulting solid is 785.398 approximately.