Question

1)The pyramid has a square base that us inscribed in the circular base of the cone. Draw an image of the composite shape of the base.

2) if the side length of the square base is 8 units long, what is the diameter of the circular base of the cone from the picture in number 1

Answer 1

Diameter of the circle is
`8√(2)` units

Explanation:

It is given that the vertices of the square fall on the circle.

So, the diagonal of the square is the diameter of the circle.

Also, the diagonal and the two sides of the square form a right angled triangle.

By Pythogoras theorem,

`hypotenuse^(2) =side^(2) +side^(2)`

=
`8^(2) +8^(2)`

=
`2(8^(2) )`

`hypotenuse=8√(2)` units

Hence, the diameter of the circle is
`8√(2)` units