Question

1. find the diameter or radius for each circle. show work!! a) circumference = 24 cm, find the diameter b) circumference = 4.1 cm, find the radius 4. show your work to find each of the following. a) diameter of a circle with a radius of 7 cm b) circumference of a circle with a radius of 7 cm c) radius of a circle with a diameter of 4.4 cm

Explanation:

Step1: Recall the formula for circumference

The formula for the circumference of a circle is $C=\pi d$, where $C$ is the circumference and $d$ is the diameter.

Step2: Solve for diameter in part a

Given $C = 24$ cm, from $C=\pi d$, we can solve for $d$ by $d=\frac{C}{\pi}$. Substituting $C = 24$ cm, we get $d=\frac{24}{\pi}\approx\frac{24}{3.14}\approx7.64$ cm.

Step3: Recall the relationship between radius and circumference

The formula for the circumference of a circle can also be written as $C = 2\pi r$, where $r$ is the radius.

Step4: Solve for radius in part b

Given $C=4.1$ cm, from $C = 2\pi r$, we solve for $r$ by $r=\frac{C}{2\pi}$. Substituting $C = 4.1$ cm, we have $r=\frac{4.1}{2\pi}\approx\frac{4.1}{2\times3.14}\approx0.65$ cm.

Step5: Recall the relationship between radius and diameter

The relationship between the radius $r$ and the diameter $d$ of a circle is $d = 2r$ or $r=\frac{d}{2}$.

Step6: Solve for diameter in part 4a

Given $r = 7$ cm, using $d = 2r$, we get $d=2\times7 = 14$ cm.

Step7: Solve for circumference in part 4b

Given $r = 7$ cm, using $C=2\pi r$, we substitute $r = 7$ cm and get $C=2\pi\times7=14\pi\approx14\times3.14 = 43.96$ cm.

Step8: Solve for radius in part 4c

Given $d = 4.4$ cm, using $r=\frac{d}{2}$, we get $r=\frac{4.4}{2}=2.2$ cm.

Answer:

a) Diameter $\approx7.64$ cm
b) Radius $\approx0.65$ cm
4a) Diameter = 14 cm
4b) Circumference $\approx43.96$ cm
4c) Radius = 2.2 cm