Axial section

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.

Correct result:

h =  10.88 cm
r =  14.51 cm

Solution:

$31^2 =h^2 + (2r)^2 \ \\ \dfrac{S_1}{S_2} = \dfrac{ 3 }{ 2 } \ \\ \dfrac{2\pi r h}{\pi r^2} = \dfrac{ 3 }{ 2 } \ \\ \dfrac{2h}{r} = \dfrac{ 3 }{ 2 } \ \\ r = \dfrac{ 2h\cdot 2 }{ 3 } \ \\ \ \\ r^2 = h^2 + 16 h^2 \cdot 2^2/3^2 = h^2(1+16\cdot 2^2/3^2) \ \\ h = \dfrac{ 31 }{ \sqrt{ 1+16\cdot 2^2/3^2}} = 10.88 \ \text{cm}$
$r = \dfrac{ 2h\cdot 2 }{ 3 } = 14.51 \ \text{cm}$

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

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

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

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

Next similar math problems:

• 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.
• Axial cut of a rectangle
Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
• Cone side
Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
• Axial section of the cone
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 of sides
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.
• Rectangle
The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
• Cylinder surface, volume
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.
• Rectangle 35
Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length.
• Roller
Cylinder shell has the same content as one of its bases. Cylinder height is 15 dm. What is the radius of the base of the cylinder?
• Rectangle - desc circle
Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter.
• Rectangle
The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
• Axial section
The axial section of the cone is an equilateral triangle with area 168 cm2. Calculate the volume of the cone.
• Rectangle diagonal
The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm2.
• Rhombus and inscribed circle
It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
• Rectangle
In a rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
• 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?
• Rectangle 3-4-5
The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.