Math help please?

Question

If someone could help with these math question I would be very thankful.

The area of a pizza is approximately 1000cm squared. Find the length of the largest cut that can be made across the pizza.

Six students share a pizza equally. The pizza has a diameter of 26cm what is the area of each slice.

Principal Smith wants to paint a large yellow circle on the school playground. She purchased a paint that indicates it can cover an area of 3 square meters. The circle must have a diameter of 3 meters. How many cans of paint will be needed.

Answer 1

Let's assume the pizza is round.

First, 1000cm^2 - We know the formula for the area of a circle is Pi*Radius^2. So...1000=Pi*R^2...Divide both sides by Pi to get R^2 gives...
R^2=318.3. To get the radius, take the square root of both sides:
R=17.8
Double that to get the diameter - the largest cut you can make across the pizza or 35.7cm.

For the 2nd one...We know the diameter is 26cm. Cut that in half to get the radius, or R=13cm.

From above, we know the area of a circle is Pi*R^2, so..pi*13^2=530.9 cm^2. Each slice is one sixth of the total area of the pizza or 530.9/6 = 88.5 cm^2.

Last, but not least, We again know the diameter - 3m. Cut that in half to get the radius: 1.5m.

Area=Pi*R^2 or A=Pi*1.5^2
which gives us: 7.1 m^2.

Each can of paint can cover 3 square meters. Two cans will only cover 6 square meters, so we'll need 3 - and we'll have leftover paint!

Hope this helps.

Orion

Answer 2

Let's do the first problem first. "The area of a pizza is approximately 1000cm squared. Find the length of the largest cut that can be made across the pizza."

We know that the area of a circle is equal to pi times the radius squared.

so A = pi*r^2

So 1000 = pi*r^2

since pi = roughly 3.1416,

1000 = 3.1416*r^2

meaning 1000 / 3.1416 = r^2

318.309142 = r^2

Since the opposite of a square is a square root, we'll take the square root of both sides, and

r = 17.8412203

Tada! Of course, we're making a cut ACROSS the pizza, so we'll double the radius, 17.84, to get the diameter, 35.68.

So the longest cut possible is roughly 35.68 centimeters!


Second problem.

"Six students share a pizza equally. The pizza has a diameter of 26cm what is the area of each slice?"

We'll find the area first, and then divide that into six equal pieces.

The diameter is 26 cm, but we need the radius to find area. So we'll cut that in half, to get a radius of 13 cm.

so we know that A = pi*13^2

We'll follow order of operations, which means that we use exponents first.

A = pi*169

since pi is roughly 3.1416,

A = 3.1416 * 169 = 530.9304,

and we'll round to 530.93.

Now we have to divide it into six pieces.

530.93 / 6 = 88.4883333 ,

so we will round it to

88.5 cm squared a piece!


Third and last.


"Principal Smith wants to paint a large yellow circle on the school playground. She purchased a paint that indicates it can cover an area of 3 square meters. The circle must have a diameter of 3 meters. How many cans of paint will be needed."

This is easier than it looks. We need to find the area first, so let's plug everything in again.

Diameter = 3, radius = 1.5

A = pi*1.5^2

A = 3.1516*2.25

A = 7.0911

Since every paint can covers three meters, she needs about two and a third paint cans (2 and a third times 3 equals 7), but you can't buy a third of a paint can!

So she'll need to buy 3 paint cans.


Hope that helps.

Just remember A = pi*r^2 , and you'll be fine.

Answer 3

#1. The longest length is the diameter of the circle. Since you have the area, you can use the area formula to solve for the diameter. Area=(pi) * radius (squared)
1000 = pi * r squared
so r = 17.84, which means the diameter = 35.68

#2. First, find the area of the whole pizza using area = pi * r^2, and then divide by 6 to get the area of each slice.

#3. Find the area of the circle that has a diameter of 3, then divide that area by 3 to get the total number of paint cans they will need.

Answer 4

1) It's asking you for the length so
Area of a circle
A=pi x radius squared
1000cm^2=3.14 x radius squared

divide both sides by 3.14
318.47 cm^2 = radius squared
then take square root

17.8 cm = radius
find diameter which is your largest length by multiplying the radius by 2
Answer= 35.6 cm

2) Find area first
Area = pi x radius squared
=3.14 x 13 x 13 (13 came from dividing the diameter by 2 to get radius)

Area = 530.66 cm^2
then divide area by 6 because pizza was shared by 6 students
Answer = 1 slice = 88.44 cm^2

3) Paint = 3 cm^2
find area of the circle
A= 3.14 x 1.5 x 1.5 (1.5 from divided diameter by 2)
A= 7.0 cm^2

take area divide by paint to get number of canes
A= 7.0 cm^2 / 3 cm^2

Answer = about 2 canes of paint

Good luck with the rest of your hwk

Answer 5

1. The area of a circle is A=pi(r^2), so plug in what you know.
1,000=pi(r^2)
1,000/pi=r^2
sqrt(1000/pi)=r
r=17.84124116
The farthest distance across a circle is the diameter, so multiply the radius by 2 to get about 35.68 cm.

2. Find the area and divide by 6.
A=pi(13^2)/6
A=pi(169)/6
A= 88.49
About 88.49 cm squared.

3. Find the area of the circle and divide by 3. Let c=cans
c=pi(1.5^2)/3
c=pi(2.25)/3
c=2.36
3 cans of paint. (You have to round up, since you can't buy 0.36 of a can of paint.)

Answer 6

#1 is a trick question. The largest cut is obviously straight across, a.k.a., the diameter. Area = 3.14 x radius squared. Divide 1000 by 3.14, then find the square root of that answer and you have the radius. Times 2 is the diameter.

Do the other two using 3.14. They're trick questions, and easier than they look.

Answer 7

formula for area of a circle: d(diameter)x3.14(pie)
sorry I would help answer but I gtg somewhere. Sorry!!!!!!!!!!!