Answer:
1. circle T with radius 8 1/2 inches ⇒ answer A
2. The area of the crust of a 15-inch pizza is 177 inches² ⇒ answer B
3. 10π feet and 31.4 feet ⇒ answers B and E
4. The better buy is 10-inch diameter pizza for $8.99 ⇒ answer A
5. The price per square inch is $0.20
6. The largest area of the pond is 1472.61 feet² ⇒ answer C
Explanation:
* Lets explain how to solve the problem
1.
- A circle is the set of all points in a plane that are a given distance
from a fixed point.
- The given distance is the radius of the circle and the fixed point
is its center
- A sphere is the set of all points in a space that are a given distance
from a fixed point.
- The given distance is the radius of the sphere and the fixed point
is its center
- A circle is 2-Dimensional, but a sphere is 3-Dimensional.
∵ The collection of all points in the same plane that means it is in a
2-D dimensional
∴ It is a circle
∵ The collection of all points in the same plane that are 8 1/2
inches from Point T
∴ The radius of the circle = 8 1/2 inches and its center is T
* circle T with radius 8 1/2 inches
2.
- The advertised size of a pizza is the diameter of the pizza
∵ The advertised size of a pizza is 15-inch pizza
∴ The diameter of the pizza is 15 inches
∵ The diameter = 2 × radius
∴ The radius = 15 ÷ 2= 7.5 inches
- The area of the circle = πr²
∴ The area of the crust = π(7.5)² = 176.7 ≅ 177 inches²
* The area of the crust of a 15-inch pizza is 177 inches²
3.
- The area of the circle is πr²
- The circumference of the circle is 2πr
- To find the circumference of the circle you must to find the radius
of the circle from its area
∵ The area of the circle is 78.5 feet²
∵ The area of the circle = πr²
∴ πr² = 78.5 ⇒ divide both sides by π
∴ r² = 78.5/π ⇒ take √ for both sides
∴ r = √(78.5/π)
∵ The circumference of the circle = 2πr
∴ The circumference of the circle = 2π × √(78.5/π) = 31.407
* The circumference of the circle ≅ 31.4 feet
∵ 10π ≅ 31.4
∴ The answer is 10π feet and 31.4 feet
4.
- To find which pizza is better buy, you must find the price per
square inch the lowest price will be better
∵ The area of the circle is πr²
∵ r = 1/2 diameter
∵ The price of the 10-inch diameter pizza is $8.99
∵ The radius of it = 1/2 × 10 = 5 inches
∴ Its area = π(5)² = 25π inches²
∵ Its price is $8.99
∴ The price per square inch = 8.99 ÷ 25π ≅ $0.11
∵ The price of the 6-inch diameter pizza is $5
∵ The radius of it = 1/2 × 6 = 3 inches
∴ Its area = π(3)² = 9π inches²
∵ Its price is $5
∴ The price per square inch = 5 ÷ 9π ≅ $0.18
∴ The price of a 10-inch diameter < the price of 6-inch diameter
∴ The better buy is 10-inch diameter pizza for $8.99
5.
∵ The area of the circle is πr²
∵ r = 1/2 diameter
∵ The cost of the circular marble tabletop is $280
∵ Its diameter is 42 inches
∵ The radius of it = 1/2 × 42 = 21 inches
∴ Its area = π(21)² = 441π inches²
∵ Its cost is $280
∴ The price per square inch = 280 ÷ 441π ≅ $0.20
* The price per square inch is $0.20
6.
∵ The pond shaped a circle
- The length of the fence is the circumference of the pond
∵ The circumference of the circle = 2πr
∵ The length of the fence is 136 feet
∴ 2πr = 136 ⇒ divide the two sides by 2π
∴ r = 136/(2π) = 68/π
∵ The area of the circle = πr²
∵ π ≅ 3.14
∴ The area of the pond = 3.14(68/3.14)² = 1472.61
∴ The largest area of the pond is 1472.61 feet²