Surrounded 8283
The cube has an edge length of 5 cm. This cube surrounds a rotating cylinder. Find the surface area of the shell and the volume of the cylinder.
Correct answer:

Tips for related online calculators
Tip: Our volume units converter will help you convert volume units.
See also our right triangle calculator.
See also our right triangle calculator.
You need to know the following knowledge to solve this word math problem:
Units of physical quantities:
Grade of the word problem:
Related math problems and questions:
- 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.
- 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?
- 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.
- Shell area cy
The cylinder has a shell area of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder.
- Rectangle 46791
We rolled up the shell of a 4 cm high rotating cylinder from a rectangle measuring 6 cm and 4 cm. Find the volume of the cylinder.
- Axial section
The axial section of the cylinder has a diagonal 40 cm. The shell size and base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder.
- Original 63974
If we reduce the length of the cube edge by 30%, this cube has a reduced surface area of 1176 cm². Find the edge length and volume of the original cube.
- Centimeters) 5540
Find the cube edge length (in centimeters) that has a surface and volume expressed by the same numeric value. Draw this cube in a ratio of 1:2.
- Cylinder 80733
How tall is a cylinder whose shell has a volume equal to the base? What is the volume of this cylinder?
- Hexagonal pyramid
Find the area of a shell of the regular hexagonal pyramid if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
- Calculate 4689
The area of the rotating cone shell is 240 cm2, and the area of its base is 160 cm². Calculate the volume of this cone.
- Calculate 82549
The cylinder has a shell surface of 88 square cm and a volume of 176 cubic cm. Calculate the radius, height, and surface area of the given solid.
- Calculate 4842
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm.
- Original 63984
If we reduce the length of the cube edge by 30%, this reduced cube has an area of 1176 cm². Specify the edge length and volume of the original cube.
- Surface area of cylinder
Determine the lateral surface of the rotary cylinder, which is a circumscribed cube with an edge length of 5 cm.
- Rotating 28501
Which bags shaped like the shell of a rotating cone can hold the most popcorn? The first bag has a height of 20 cm, and the length of its side is 24 cm. The second bag has a base radius of 10 cm and a height of 25 cm.
- Cylinder surface, volume
The area of the base and the area of the shell are in the ratio of 3:5. Its height is 5 cm less than the radius of the base. Calculate both surface area and volume.