Question

40. Circle A has a radius 4 inches. Is each statement about circle A true?

Answer 1

The first statement is about the diameter of the circle.

The diameter of a circle is always the double of its radius.

So if circle A ras a radius of 4 inches, its diameter is:

`\text{diameter}=2\cdot\text{radius}=2\cdot4=8\text{ inches}`

So the first statement is true (YES)

The second statement is about the area of the circle. The area of a circle is given by the following equation:

`Area=\pi\cdot r^2`

If the radius of the circle is 4 inches, we have:

`\text{Area}=\pi\cdot4^2=16\pi`

So the second statement is also true (YES)

The third statement is about the volume of a cylinder with a height of 6 inches and the circle A as the base. The volume of a cylinder is given by the equation:

`\text{Volume}=\pi\cdot r^2\cdot h`

Using the radius = 4 inches and the height = 6 inches, we have:

`\begin{gathered} \text{Volume}=\pi\cdot4^2\cdot6 \\ \text{Volume}=\pi\cdot16\cdot6=96\pi \end{gathered}`

The volume is not 64pi, so this statement is false (NO).