# Cylinder diameter

The surface of the cylinder is 149 cm2. The cylinder height is 6 cm. What is the diameter of this cylinder?

Result

D =  5.439 cm

#### Solution:

$S = 2\pi r^2 + 2\pi r h \ \\ S = \pi D^2/2 + \pi D h \ \\ \ \\ \pi D^2/2 + \pi D h - S = 0 \ \\ \pi D^2/2 + \pi \cdot 6 \cdot D - 149 = 0 \ \\ \ \\ 1.57079632679D^2 +18.85D -149 =0 \ \\ \ \\ a=1.57079632679; b=18.85; c=-149 \ \\ D = b^2 - 4ac = 18.85^2 - 4\cdot 1.57079632679 \cdot (-149) = 1291.50036921 \ \\ D>0 \ \\ \ \\ D_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ -18.85 \pm \sqrt{ 1291.5 } }{ 3.14159265359 } \ \\ D_{1,2} = -6 \pm 11.4392458704 \ \\ D_{1} = 5.43924587037 \ \\ D_{2} = -17.4392458704 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 1.57079632679 (D -5.43924587037) (D +17.4392458704) = 0 \ \\ \ \\ D>0 \ \\ D \doteq 5.439 \ \text{cm}$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators

## Next similar math problems:

1. Kitchen
Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
2. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
3. Reciprocal equation 2
Solve this equation: x + 5/x - 6 = 4/11
4. Discriminant
Determine the discriminant of the equation: ?
Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
6. Equation
Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
7. Roots
Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
8. Variations 4/2
Determine the number of items when the count of variations of fourth class without repeating is 600 times larger than the count of variations of second class without repetition.
Which of the points belong function f:y= 2x2- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
10. Combinations
How many elements can form six times more combinations fourth class than combination of the second class?
11. Combinations
From how many elements we can create 990 combinations 2nd class without repeating?
12. Solve 3
Solve quadratic equation: (6n+1) (4n-1) = 3n2
13. Cinema 4
In cinema are 1656 seats and in the last row are 105 seats , in each next row 3 seats less. How many are the total rows in cinema?
14. 2nd class combinations
From how many elements you can create 4560 combinations of the second class?
15. Median
The number of missed hours was recorded in 11 pupils: 5,12,6,8,10,7,5,110,2,5,6. Determine the median.
16. Sequence
Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
17. Calculation of CN
Calculate: ?