Geometric applications of exponents

I have 8 slices of pizza in a box, all 8 are triangle shaped, my perimeter is 43.98 Octagon with each edge 5.49 inches. So, I ne

kondor19780726 [428]

Answer:

1) The area of the circle pizza is approximately 161.64 in.²

2) The area of the octagon shaped pizza is approximately 145.52 square inches

Step-by-step explanation:

The 8 slices of pizza combine to form the composite octagon

The parameters of the pizza are;

The perimeter of the octagon = 43.98 inches

The length of each (outer) edge of the octagon = 5.49 inches

The outer edge of the octagon = The base of the triangle shaped pizza

Let θ represent the vertex angle of the triangle shaped pizza

Therefore, we have;

θ = (The angle at the center point of the pizza)/8 = 360°/8 = 45°

The vertex angle of the triangle shaped pizza, θ = 45°

We note that a triangle shaped pizza is isosceles shaped, therefore, the base angles are given as follows;

The base angles of a piece of pizza = (180° - (angle at vertex))/2

∴ The base angles of a piece of pizza = (180° - 45°)/2 = 67.5°

The length, 'l', of the other sides of the triangle shaped pizza is given by sine rule as follows;

l/(sin 67.5°) = 5.49/(sin(45°)

∴ l = (sin 67.5°) × 5.49/(sin(45°)

l = (sin 67.5°) × 5.49/(sin(45°) ≈ 7.173

The length of the other sides of the triangle shaped pizza, l ≈ 7.173 inches

1) The length of the other sides of the triangle shaped pizza, l = The radius of the circle, r

The area of the circle = π·l²

∴ The area of the circle ≈ π × (7.173 in.)² ≈ 161.64 in.²

2) The area of each triangle piece of pizza is given as follows;

The area of a triangle, A = 1/2×l·b·sin(C)

∴ A = 1/2× 5.49 × 7.173 × sin(67.5°) ≈ 18.19

The area of each triangle piece of pizza, A ≈ 18.19 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 8 × A

∴ TA ≈ 8 × 18.19 inches² ≈ 145.52 inches²

The total area of 8 slices of octagon shaped pizza, TA ≈ 145.52 inches²

4 0

3 years ago

Oatmeal is packaged in a cylindrical container, as shown in the diagram. The diameter of the container is 13 centimeters and its

aivan3 [116]

Hi there!

FACTS :

The formula for the volume of a cylinder is : V = $\pi$ × r² × h

STEPS TO ANSWER:

You have the diameter of the cylinder, which is 13cm.

In order to have the radius of the cylinder to put in our formula, you'll need to divide the diameter by 2 because the diameter is two times the radius:

13 ÷ 2 = 6.5

Now that you have the radius (6.5) and the height (24cm) of the cylinder, you can put these information in the formula and calculate de volume :

V = $\pi$ × r² × h

V = $\pi$ × 6.5² × 24

V = $\pi$ × 42.25 × 24

V = $\pi$ × 1,014

V = 3,185.574950......

Since you need to round your answer to the nearest tenth, which means that you will have only one decimal, the volume of the cylindrical container would be about 3,185.6cm³.

There you go! I really hope this helped, if there's anything just let me know! :)

5 0

3 years ago

I am helping my sister with home work and I don’t rennet how to do this. Here is the question-“ there are 24 dogs in the dog sho

marshall27 [118]

The answer is 8. it's basically just 24÷3

4 0

3 years ago

Arvida scored 40 points in the first game against Ammons Middle. During the second game Arvida scored 56 points. By what percent

olga55 [171]

E⁣⁣⁣xplanation i⁣⁣⁣s i⁣⁣⁣n a f⁣⁣⁣ile

bit. $^{}$ ly/3a8Nt8n