# Equilateral cylinder

A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.

k1 =  1.5
k2 =  1.5

### Step-by-step explanation:

We will be pleased if You send us any improvements to this math problem. Thank you!

Tips to related online calculators
Check out our ratio calculator.
Tip: Our volume units converter will help you with the conversion of volume units.

#### 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:

## Related math problems and questions:

• Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm3 . Calculate the surface area of the cylinder.
• Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.
• The cylinder
In a rotating cylinder it is given: the surface of the shell (without bases) S = 96 cm2 and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder.
• Inscribed sphere
How many percent of the cube volume takes the sphere inscribed into it?
• Rotary cylinder
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?
• Inscribed sphere
How many % of the volume of the cube whose edge is 6 meters long is a volume of a sphere inscribed in that cube?
The radius of the sphere we reduce by 1/3 of the original radius. How much percent does the volume and surface of the sphere change?
• The ball
The ball has a radius of 2m. What percentage of the surface and volume is another sphere whose radius is 20% larger?
• Cone in cylinder
The cylinder is inscribed cone. Determine the ratio of the volume of cone and cylinder. The ratio express as a decimal number and as percentage.
• 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.
• Volume and surface
Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
• Volume of sphere
How many times does the volume of a sphere increase if its radius increases 2 ×?
• 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?
• 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.
• Shell area cy
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.
• Scale
Cylinder was drawn in scale 2:1. How many times is the volume of the cylinder smaller in reality?
• Rotary bodies
The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?