1 Answer

Franz Gastring · Answer 1 · 2023-07-18T11:14:35+0000

Answer:

Using 22/7 as pi, the area of a circle with a diameter of 14 metres is:

154 m²

Explanation:

To solve, use the formula for the area of a circle.

Formula for area of a circle

Remember the formula for area of a circle. Be careful not to mix up the formula for area with the formula for circumference!

$A = \pi r^(2)$

From the question, we know:

To use the formula, we need the radius ("r").

The radius is a line that goes from the centre point of the circle to the circle outline. It is half the length of the diameter.

The diagram shows the diameter ("d"), which goes through the centre point of the circle. It is twice the length of the radius.

Solve for "r".

r = d/2

r = (14 m)/2

r = 7 m

Substitute r = 7 m and π = 22/7 into the formula for the area of a circle.

$A = \pi r^(2)$ Start with the formula and substitute.

$\displaystyle{A = (22)/(7) (7\ m)^(2)}$ Square "7" and the "m".

Remember that the answer for area is always squared units.

$\displaystyle{A = (22)/(7) (49\ m^(2))}$

Multiplying a fraction and whole number is the same as multiplying the whole number in the numerator (top of the fraction).

$\displaystyle{A = (22*49)/(7)m^(2)}$ Simplify the numerator.

$\displaystyle{A = (1078)/(7)m^(2)}$ Divide.

$A = 154\ m^(2)$ Final answer

∴ The area of the circle is 154 m².