Question

4 work out the area of each circle (use the π button on your calculator. round your answers correct to 3 significant figures (3 s.f.).
a radius = 6cm
b radius = 4.25m
c diameter = 23 cm
d diameter = 4.8m

Explanation:

Part a

Step1: Recall the formula for the area of a circle

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

Step2: Substitute the radius value

Given \( r = 6\space\text{cm} \), substitute into the formula: \( A=\pi\times(6)^{2}=\pi\times36 \)

Step3: Calculate the area

Using the \(\pi\) button on the calculator, \( A = 36\pi\approx113.097\space\text{cm}^2\)

Step4: Round to 3 significant figures

\( 113.097\approx113\space\text{cm}^2\) (to 3 s.f.)

Part b

Step1: Recall the formula for the area of a circle

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

Step2: Substitute the radius value

Given \( r = 4.25\space\text{m} \), substitute into the formula: \( A=\pi\times(4.25)^{2}=\pi\times18.0625 \)

Step3: Calculate the area

Using the \(\pi\) button on the calculator, \( A=18.0625\pi\approx56.745\space\text{m}^2\)

Step4: Round to 3 significant figures

\( 56.745\approx56.7\space\text{m}^2\) (to 3 s.f.)

Part c

Step1: Find the radius from the diameter

The radius \( r \) is half of the diameter \( d \), so \( r=\frac{d}{2} \). Given \( d = 23\space\text{cm} \), then \( r=\frac{23}{2}=11.5\space\text{cm} \)

Step2: Recall the formula for the area of a circle

The formula for the area of a circle is \( A=\pi r^{2} \)

Step3: Substitute the radius value

Substitute \( r = 11.5\space\text{cm} \) into the formula: \( A=\pi\times(11.5)^{2}=\pi\times132.25 \)

Step4: Calculate the area

Using the \(\pi\) button on the calculator, \( A = 132.25\pi\approx415.475\space\text{cm}^2\)

Step5: Round to 3 significant figures

\( 415.475\approx415\space\text{cm}^2\) (to 3 s.f.)

Part d

Answer:

s:
a. \(\boldsymbol{113\space\text{cm}^2}\)
b. \(\boldsymbol{56.7\space\text{m}^2}\)
c. \(\boldsymbol{415\space\text{cm}^2}\)
d. \(\boldsymbol{18.1\space\text{m}^2}\)