Question

How do you find the circumference and the area of a circle with diameter 2ft?

Answer 1

Hint: In this problem, we have to find the area and the circumference of the circle whose given diameter is 2 ft. We know that the formula for the area of a circle is \[\pi {{r}^{2}}\] and the circumference of the circle is \[2\pi r\]. We can see that the formula requires the value of the radius. We can find the value of the radius from the given diameter as the radius is half of the diameter.

Complete step by step solution:
We know that the given diameter is 2ft.
We also know that radius is half of the diameter,
Diameter = 2ft
Radius = \[\dfrac{2}{2}=1\]ft.
We know that the formula for area of circle is,
Area of circle = \[\pi {{r}^{2}}\]= \[\pi \times 1=3.14\]square feet
We know the formula for the circumference of the circle,
The circumference of the circle = \[2\times \pi \times 1=2\times 3.14=6.24\]feet.
Therefore, the area of the circle whose diameter is 2ft is 3.14 square feet and the circumference of the circle whose diameter is 2ft is 6.24 feet.
We can now draw the diagram for the given circle with diameter 2ft whose circumference is 6.24 feet and area is 3.14 square feet.

Note: Students make mistakes while finding the radius from the given diameter. We should always remember that diameter is twice the radius and radius is half of the diameter. We should also know geometric formulas such as area of circle and circumference of the circle. We should know the value of \[\pi \] to solve these types of problems.