I added 18 to 3 times a number, the result is equal to 5 times the number. What is the number.
What is the volume of a cylinder of base radius 5cm and height 14cm?
```
-----------------------------
| * |
| * * |
| * * |
| * * |
| * * | 14cm
| * * |
| *-------------*---- |
| 14 cm |
-----------------------------
```
A) The diameter of the base is 14cm, so the radius is half of this, which is `r = 7cm`. The formula for the circumference of a circle is `C = 2πr`, so we can substitute the value of `r` and approximate π as `22/7` to find the circumference, giving:
C = 2πr
C = 2 × (22/7) × 7cm
C = 44cm
Therefore, the circumference of the base is 44cm.
B) The area of the base of a cylinder is given by the formula `A = πr²`, so we can substitute the value of `r` and approximate π as `22/7` to find the area of the base, giving:
A = πr²
A = (22/7) × 7cm²
A = 22cm²
Therefore, the area of the base of the cylinder is 22 square centimeters (cm²).
C) The formula for the volume of a cylinder is `V = πr²h`, so we can substitute the value of `r`, `h`, and approximate π as `22/7` to find the volume, giving:
V = πr²h
V = (22/7) × 7cm² × 14cm
V = 22 × 7 × 2
V = 308cm³
Therefore, the volume of the cylinder is 308 cubic centimeters (cm³).
D) The curved surface area of a cylinder is given by the formula `A = 2πrh`, so we can substitute the values of `r`, `h`, and approximate π as `22/7` to find the curved surface area, giving:
A = 2πrh
A = 2 × (22/7) × 7cm × 14cm
A = 2 × 22 × 2 × 7
A = 616cm²
Therefore, the curved surface area of the cylinder is 616 square centimeters (cm²).
E) The total surface area of a cylinder is the sum of the curved surface area and the area of the two circular bases. We already found the formula for the curved surface area in part D. The formula for the area of a circle is `A = πr²`, so we can substitute the value of `r` and approximate π as `22/7` to find the area of each circular base, giving:
A = πr²
A = (22/7) × (7cm/2)²
A = 22/7 × 49/4
A = 38.5 cm² (approx)
Therefore, the total surface area of the cylinder is:
A = 2πrh + 2πr²
A = 2 × (22/7) × 7cm × 14cm + 2 × (22/7) × (7cm/2)²
A = 2 × 22 × 2 × 7 + 2 × 22/7 × 49/4
A = 1232/7 + 77/2
A ≈ 247.14cm²
Therefore, the total surface area of the cylinder is approximately 247.14 square centimeters (cm²).
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Calculate the angle of elevation of a man 6m away from the base of a tree 8m tall.
A cylindrical tank of storing oil has a capacity of 1078m².if it's height and it's radius are equal, calculate the depth of oil in the tank when full.
Let's call the height (and radius) of the cylindrical tank "h". We can use the formula for the volume of a cylinder to find the height required to store 1078m³ of oil:
```
volume = πr²h
1078 = πh²h
```
Simplifying the right side:
```
1078 = πh³
```
Solving for h:
```
h³ = 1078/π
h³ ≈ 343.35
h ≈ 7.8
```
Therefore, the height (and radius) of the cylindrical tank is approximately 7.8m. When the tank is full, the depth of oil will also be 7.8m.
5x-2y=11.......
4x-3y=6........
We can solve this system of equations using either substitution or elimination.
**Using Substitution:**
Let's use the first equation to solve for one of the variables in terms of the other.
```
5x - 2y = 11
5x = 2y + 11
x = (2y + 11)/5
```
Now we can substitute this expression for x into the second equation:
```
4x - 3y = 6
4((2y + 11)/5) - 3y = 6
(8y + 44)/5 - 3y = 6
8y + 44 - 15y = 30
-7y = -14
y = 2
```
Now that we know y = 2, we can substitute this value into one of the original equations to solve for x:
```
5x - 2y = 11
5x - 2(2) = 11
5x - 4 = 11
5x = 15
x = 3
```
Therefore, the solution to the system of equations is x = 3 and y = 2.
**Using Elimination:**
Let's multiply the first equation by 3 and the second equation by 2 to create opposite coefficients for y:
```
15x - 6y = 33
8x - 6y = 12
```
Now we can subtract the second equation from the first to eliminate y:
```
15x - 8x = 33 - 12
7x = 21
x = 3
```
Substituting x = 3 into one of the original equations:
```
5x - 2y = 11
5(3) - 2y = 11
15 - 2y = 11
-2y = -4
y = 2
```
Therefore, the solution to the system of equations is x = 3 and y = 2.
The formula for the volume of a cylinder is:
`V = πr²h`
where `r` is the radius of the base of the cylinder, `h` is the height of the cylinder, and `π` is a mathematical constant approximately equal to 3.14159.
In this case, we have `r = 5cm` and `h = 14cm`, so we can substitute these values into the formula and calculate the volume:
`V = πr²h`
`V = π(5cm)²(14cm)`
`V = π(25cm²)(14cm)`
`V = 3.14159(350cm³)`
`V ≈ 1099.11cm³`
Therefore, the volume of the cylinder is approximately 1099.11 cubic centimeters (cm³).
In the diagram below, the cylinder has diameter of 14cm and height of 14cm.
A)find the circumference of the base.
B) find the area of the base.
C) what is the volume of the cylinder.
D) find the curve surface area of the cylinder.
E) find the total surface area of the cylinder.(Take π=22÷7)