Axial section

Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2.

Calculate the volume and surface area of this cylinder.

Correct answer:

S =  3855.98 cm2
V =  15473.44 cm3

Step-by-step explanation:

402=h2+(2r)2 S1S2=32 2πrhπr2=32 2hr=32 r=2h23  r2=h2+16h222/32=h2(1+1622/32) h=401+1622/32=14.045 cm r=2h23=18.727 cm  S=2πr2+2πrh=3855.98 cm2 
V=πr2h=15473.44 cm3



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar







Tips to related online calculators
Check out our ratio calculator.
Pythagorean theorem is the base for the right triangle calculator.

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

Related math problems and questions:

  • Axial section
    cylinder_cut The axial section of the cylinder has a diagonal 31 cm long, and we know that the area of the side and the base area is in ratio 3:2. Calculate the height and radius of the cylinder base.
  • Axial cut of a rectangle
    cylinder_cut Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
  • Axial section of the cone
    rez_kuzel The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
  • Ratio-cuboid
    hranol222 The lengths of the edges of the cuboid are in the ratio 2: 3: 6. Its body diagonal is 14 cm long. Calculate the volume and surface area of the cuboid.
  • Cylinder surface, volume
    cyl The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder.
  • Shell area cy
    valec The cylinder has a shell content of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
  • Equilateral cylinder
    3d Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
  • Axial section
    kuzel_rs Calculate the volume and surface of a cone whose axial section is an equilateral triangle with side length a = 18cm.
  • Cuboid diagonals
    kvadr_diagonal The cuboid has dimensions of 15, 20 and 40 cm. Calculate its volume and surface, the length of the body diagonal and the lengths of all three wall diagonals.
  • Rotary cylinder
    Povrchy_a_objemy_telies The rotating cylinder has a surface area of 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
  • The sides
    rectangles The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals
  • Surface of the cylinder
    valec Calculate the surface of the cylinder for which the shell area is Spl = 20 cm2 and the height v = 3.5 cm
  • Axial section
    cone2 The axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
  • Solid cuboid
    cuboid A solid cuboid has a volume of 40 cm3. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.
  • Cylinder - basics
    cylinder Cylinder with base radius r = 54 cm and height h=35 cm. Calculate: a) Area of the base
  • Cone and the ratio
    kuzel The rotational cone has a height 43 cm, and the ratio of the base surface to lateral surface is 5: 7. Calculate the surface of the base and the lateral surface.
  • Cuboid face diagonals
    face_diagonals_1 The lengths of the cuboid edges are in the ratio 1: 2: 3. Will the lengths of its diagonals be the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid.