Question

what is the area of a circle with
given measure
a radius of 4cm a=π×4²=π×16=16π cm²
for a diameter of 22
a diameter of 22cm \frac{22}{2}=11cm
a=π×11²=π×121=121π cm (take π=\frac{22}{7})
a circumference of 98cm
a circumference of 98cm

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \), where \( r \) is the radius of the circle. If the diameter \( d \) is given, the radius \( r=\frac{d}{2} \).

Step2: Analyze each case

• Case 1: Radius \( r = 4\space\text{cm}\)

Using the formula \( A = \pi r^{2} \), substitute \( r = 4 \):
\( A=\pi\times(4)^{2}=\pi\times16 = 16\pi\space\text{cm}^2\) (or approximately \( 50.24\space\text{cm}^2 \) if \( \pi\approx3.14 \)).

• Case 2: Diameter \( d = 22\space\text{cm}\)

First, find the radius: \( r=\frac{d}{2}=\frac{22}{2}=11\space\text{cm} \).
Then, use the area formula: \( A=\pi r^{2}=\pi\times(11)^{2}=121\pi\space\text{cm}^2\) (or approximately \( 379.94\space\text{cm}^2 \) if \( \pi\approx3.14 \)).

• Case 3: Circumference \( C = 9\pi\space\text{cm}\)

The formula for circumference is \( C = 2\pi r \). Solve for \( r \):
\( 9\pi=2\pi r\implies r=\frac{9\pi}{2\pi}=\frac{9}{2}=4.5\space\text{cm} \).
Now, find the area: \( A=\pi r^{2}=\pi\times(4.5)^{2}=20.25\pi\space\text{cm}^2\) (or approximately \( 63.585\space\text{cm}^2 \) if \( \pi\approx3.14 \)).

• Case 4: Circumference \( C = 2\pi\space\text{cm}\)

Using \( C = 2\pi r \), solve for \( r \):
\( 2\pi=2\pi r\implies r = 1\space\text{cm} \).
Then, the area: \( A=\pi r^{2}=\pi\times(1)^{2}=\pi\space\text{cm}^2\) (or approximately \( 3.14\space\text{cm}^2 \) if \( \pi\approx3.14 \)).

Answer:

• For radius \( 4\space\text{cm} \): \( \boldsymbol{16\pi\space\text{cm}^2} \) (or \( \boldsymbol{50.24\space\text{cm}^2} \))
• For diameter \( 22\space\text{cm} \): \( \boldsymbol{121\pi\space\text{cm}^2} \) (or \( \boldsymbol{379.94\space\text{cm}^2} \))
• For circumference \( 9\pi\space\text{cm} \): \( \boldsymbol{20.25\pi\space\text{cm}^2} \) (or \( \boldsymbol{63.585\space\text{cm}^2} \))
• For circumference \( 2\pi\space\text{cm} \): \( \boldsymbol{\pi\space\text{cm}^2} \) (or \( \boldsymbol{3.14\space\text{cm}^2} \))