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=2πr2+2πrh S=πD2/2+πDh  πD2/2+πDh−S=0 πD2/2+π⋅6⋅D−149=0  1.57079632679D2+18.85D−149=0  a=1.57079632679;b=18.85;c=−149 D=b2−4ac=18.852−4⋅1.57079632679⋅(−149)=1291.50036921 D>0  D1,2=−b±D2a=−18.85±1291.53.14159265359 D1,2=−6±11.4392458704 D1=5.43924587037 D2=−17.4392458704   Factored form of the equation:  1.57079632679(D−5.43924587037)(D+17.4392458704)=0  D>0 D≐5.439 cmS = 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}

Try another example


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...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  1. Kitchen
    valcek_na_cesto Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
  2. Theorem prove
    thales_1 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
    parabola2 Solve this equation: x + 5/x - 6 = 4/11
  4. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  5. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  6. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  7. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  8. Variations 4/2
    pantagram_1 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.
  9. Quadratic function 2
    parabola1 Which of the points belong function f:y= 2x2- 3x + 1 : A(-2, 15) B (3,10) C (1,4)
  10. Combinations
    trezor_1 How many elements can form six times more combinations fourth class than combination of the second class?
  11. Combinations
    math_2 From how many elements we can create 990 combinations 2nd class without repeating?
  12. Solve 3
    eq2_4 Solve quadratic equation: (6n+1) (4n-1) = 3n2
  13. Cinema 4
    cinema_2 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
    color_circle From how many elements you can create 4560 combinations of the second class?
  15. Median
    statistics 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
    sunflower Between numbers 1 and 53 insert n members of the arithmetic sequence that its sum is 702.
  17. Calculation of CN
    color_combinations Calculate: ?