If the radius of a pizza is 20 cm, what is the central angle in degrees that gives one person 30 cm of crust?

Question 5 options:

a) 120°

b) 35°

c) 43°

d) 86°

I say option a, but my partner disagrees

nvm we figured out it's d)

Well, pizza debates are no joke, huh? Let me help you settle this crusty argument.

The circumference of a circle is given by the formula 2πr, where r is the radius. In this case, with a radius of 20 cm, the circumference of the pizza is 2π(20) = 40π cm.

Now, if one person wants 30 cm of crust, we can find the central angle using proportions. Since the whole circumference is 360°, we have the following:

30 cm crust = x° central angle
40π cm crust = 360° central angle

To solve for x°, we set up the proportion:

30/(40π) = x/360

Now, let me crunch the numbers... *humming circus music*... *tapping on my calculator*... *making funny faces*...

And the answer burps out as approximately 43°! So, option c) 43° is your crusty winner!

But hey, disagreements are part of the pizza experience, so maybe you and your partner can compromise and enjoy a delightful 120° of pizza together! Who doesn't love a big slice, right?

To find the central angle that gives one person 30 cm of crust on a pizza with a radius of 20 cm, we can use the formula:

Crust Length = circumference of the pizza / central angle

First, let's calculate the circumference of the pizza using the formula:

Circumference = 2 * π * radius

Circumference = 2 * π * 20 cm
Circumference ≈ 125.66 cm

Now let's substitute the crust length and circumference into the formula to solve for the central angle:

30 cm = 125.66 cm / central angle

To isolate the central angle, let's rearrange the equation:

central angle = 125.66 cm / 30 cm
central angle ≈ 4.19

Since we need to find the angle in degrees, we multiply the result by 360 degrees (as there are 360 degrees in a circle):

central angle ≈ 4.19 * 360
central angle ≈ 150.84°

Therefore, the central angle that gives one person 30 cm of crust on a pizza with a radius of 20 cm is approximately 150.84°. Since option a) is closest to this value, it is the correct answer.

To solve this problem, we need to find the central angle that gives one person 30 cm of crust on the pizza with a radius of 20 cm.

First, let's find the circumference of the pizza using the formula:
Circumference = 2 × pi × radius
C = 2 × 3.14 × 20
C = 125.6 cm

Next, let's find the portion of the pizza's circumference that represents 30 cm of crust.

Proportion = (Length of desired portion) / (Total length)
Proportion = 30 cm / 125.6 cm
Proportion ≈ 0.2386

Now, we need to find the central angle that corresponds to this proportion.

Central angle = Proportion × 360°
Central angle ≈ 0.2386 × 360°
Central angle ≈ 86.1°

Therefore, the central angle that gives one person 30 cm of crust is approximately 86.1° which corresponds to option d) 86°. So, your partner is correct.