A cylinder

A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the top and bottom. (forming a spiral around the cylinder).
How long is the string in cm?

Correct result:

x =  180 cm

Solution:

h=108 cm c=24 cm  c=2π r r=c/(2π)=24/(2 3.1416)3.8197 cm  x=h2+(6 c)2=1082+(6 24)2=180 cm



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 2 comments:
#
Dr Math
Finding the length of the string is the same as finding the length of the hypotenuse of a triangle with a height of 48 cm and a base of a number of turns*circumference

#
Math student
Can u put this in sixth grade math terms

avatar









Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Cylinder and its circumference
    cylinder If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?
  • Circle described
    described_circle_right_triangle The radius of the circle described to the right triangle with 6 cm long leg is 5 cm. Calculate the circumference of this triangle.
  • Ratio of sides
    described_circle2 Calculate the area of a circle with the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
  • Perimeter of base
    valec_16 The circumference of the base of the rotating cylinder is same as its height. What is the diameter and height of this cylinder with volume 1 liter?
  • Hexagon cut pyramid
    truncated_hexa_pyramid Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm.
  • Rectangle diagonals
    rectangle_diagonals_1 It is given rectangle with area 24 cm2 a circumference 20 cm. The length of one side is 2 cm larger than length of second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers.
  • Cap
    cone_hat Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 cm.
  • Concentric circles and chord
    tetiva2 In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?
  • Total displacement
    stroke_bore_engine Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back t
  • Arm and base
    rr_triangle3 The isosceles triangle has a circumference of 46 cm. Calculate its area if the arm is 5 cm longer than the base.
  • The diagonals
    kosostvorec The diagonals of the KOSA diamond are 20 cm and 48 cm long. Calculate the circumference of the diamond in centimeters rounded to one unit.
  • Two chords
    twochords In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.
  • Pentagon
    5gon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
  • Right triangle
    rt_triangle_1 A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?
  • Medians in RT
    right_triangle The rectangular triangle ABC has a length of 10 cm and 24 cm. Points P, Q, R are the centers of the sides of this triangle. The perimeter of the PQR triangle is:
  • Perimeter and legs
    RT_triangle Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.
  • Ratio of sides
    trojuholnik_5 The triangle has a circumference of 21 cm and the length of its sides is in a ratio of 6: 5: 3. Find the length of the longest side of the triangle in cm.