Find the volume of the rim of a fly wheel its mean radius being 10 feet its section being a square whose side is 1. 3 feet. Assume PI=3.1412. Your answer should be correct to one decimal. (In cubic feet)
Answers
Answer:
Cube the Radius
Cube the radius or, to put it another way, multiply the radius by itself three times. So if the radius of your sphere is 4 feet, you'd have:
(4\text{ feet})^3=4\text{ feet}\times 4\text{ feet}\times 4\text{ feet}=64\text{ feet}^3(4 feet)
3
=4 feet×4 feet×4 feet=64 feet
3
Simplify the Equation
Simplify the right side of the equation. Most teachers will let you substitute 3.14 for the value of pi, which gives you:
A = 3.14 × (20 \text{ ft})^2A=3.14×(20 ft)
2
Which then simplifies to:
A = 3.14 × 400 \text{ ft}^2A=3.14×400 ft
2
And finally:
A = 1256\text{ ft}^2A=1256 ft
2
This is the area of your circle.
Calculating Circumference From Diameter
If you know the circle's diameter, multiply that number by π (pi) to get the circle's circumference. The value of π has been calculated to more than 22 trillion digits, but most teachers will let you abbreviate it to 3.14. Sometimes for construction or engineering work – or simply for the sake of the challenge – you may be asked to use 3.1416 or perhaps even more digits. So if the diameter of your circle is 10 feet, you'd calculate:
10 × 3.14 = 31.4 \text{ feet}10×3.14=31.4 feet
as the circumference, or
10 × 3.1416 = 31.416 \text{ feet}10×3.1416=31.416 feet
if you're asked for a more exact answer.
Calculating Circumference From Radius
If you only know the radius of the circle, you're in luck: The radius is always half the diameter. So multiply that radius by 2, and then multiply the result by π to get the circle's circumference. If the radius of your circle is 3 feet, for example, its diameter is 3 × 2 = 6 feet; and the circumference is then:
6 × 3.14 = 18.84 \text{ feet}6×3.14=18.84 feet
Or
6 × 3.1416 = 18.8496 \text{ feet}6×3.1416=18.8496 feet
Area of a Circle
Measure the radius of the circle with a ruler.
Square the radius. For example, if the radius equals 3 yards, multiply 3 yards by 3 yards to get 9 square yards.
Multiply the result by pi, approximately 3.14, to find the area of a circle. Completing the example, multiply 9 square yards by 3.14 to find the area of the circle equals 28.26 square yards.
Volume of a Sphere
Cube the radius of the sphere. To "cube" a number means to multiply it by itself, and then do it again. For example, if the radius equals 3 yards, multiply 3 yards by 3 yards to get 9 square yards, then multiply 9 square yards by 3 yards to get 27 cubic yards.
Multiply the result by pi, approximately 3.14. In this example, multiply 27 cubic yards by 3.14 to get 84.78 cubic yards.
Multiply the result by 4/3 to find the volume of the sphere in cubic yards. Completing the example, multiply 84.78 by 4/3 to get 113.04 cubic yards.
Step-by-step explanation:
Given:-
the rim of a fly wheel its mean radius being 10 feet its section being a square whose side is 1. 3 feet. Assume PI=3.1412
To find:-
Find the volume of the rim of a fly wheel
Solution:-
Mean radius of the rim of the fly wheel = 10 feet
its section being a square whose side is 1. 3 feet.
=>Thickness of the rim = 1.3 feet
The radius of the outside of the fly wheel
=>Mean radius + Thickness/2
=>10+(1.3/2)
=>10+0.65
=>10.65 feet
The inner edge of the rim from the axle =
Mean radius -Thickness /2
=>10-(1.3/2)
=>10 -0.65
=>9.35 feet
Now we have
The radius of the outside of the fly wheel
= Radius of the cylinder shaped circular hole in the middle = 10.65 feet
The inner edge of the rim from the axle =
Radius of the cylinder shaped circular hole in the middle = 9.35 feet
We know that
Volume of a cylinder = πr^2 h cubic units
We have r = 10.65 feet and h = 1.3 feet
Volume of the out side of the wheel =
π(10.65)^2×(1.3)
=>V1 = π×113.4225×1.3
=>V1 = 147.44925π cubic feet -----(2)
Volume of a cylinder = πr^2 h cubic units
We have r = 9.35 feet and h = 1.3 feet
Volume of the Inner of the wheel
=>V2 = π×(9.35)^2×1.3
=>V2 = π×87.4225×1.3
=>V2 = 113.64925π cubic feet ------(3)
Now
Volume of the rim
=>Volume of the Outside of the wheel - Volume of the inside of the wheel
=>V1-V2
=>147.44925π cubic feet - 113.64925π cubic feet
=> 33.8 π cubic feet
On Substituting the value of π=3.1412 (given )
=>33.8×3.1412
=>106.17256 cubic feet
=>106.2 cubic feet (correct it one decimal)
Answer:-
The volume of the rim of the fly wheel
= 106.2 cubic feet
Used formulae:-
Volume of a cylinder = πr^2 h cubic units
Where r is the radius and h is the height of the cylinder