Height as diameter of base

The rotary cylinder has a height equal to the base diameter and the surface of 471 cm². Calculate the volume of a cylinder.

Correct result:

V =  784.801 cm³

Solution:

$$\begin{gathered} S=471{\text{cm}}^2 \\ h=D \\ h=2r \\ S=2\pi r^2+2\pi rh \\ S=2\pi r^2+4\pi r^2 \\ S=6\pi r^2 \\ r=\sqrt{S\mathrm{/}(6\pi )}=\sqrt{471\mathrm{/}(6\cdot 3.1416)}\doteq 4.9987\text{ cm } \\ h=2\cdot r=2\cdot 4.9987\doteq 9.9975\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 4.9987^2={\displaystyle \frac{157}{2}}=78\frac{1}{2}=78.5{\text{cm}}^2 \\ {S}_2=2\cdot S_1+2\pi \cdot r\cdot h=2\cdot 78.5+2\cdot 3.1416\cdot 4.9987\cdot 9.9975=471{\text{cm}}^2 \\ {S}_2=S \\ V=S_1\cdot h=78.5\cdot 9.9975=784.801{\text{cm}}^3 \end{gathered}$$

Try another example

Showing 0 comments:

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.
• Diameter = height
  The surface of the cylinder, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
• Rotary cone
  Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm³. Calculate the radius of the base circle and height of the cone.
• Cylinder - h
  Cylinder volume is 215 cm³. Base radius is 2 cm. Calculate the height of the cylinder.
• 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?
• 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.
• Cylinder height
  Calculate the height of the cylinder and its surface is 2500 dm² and the bases have a diameter 5dm.
• Cylinder
  The cylinder surface is 922 dm², its height is equal to the radius of the base. Calculate height of this cylinder.
• Tetrahedral prism - rhomboid base
  Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm.
• Quadrilateral pyramid,
  A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
• The hollow cylinder
  The hollow cylinder has a height of 70 cm, an outer diameter of 180 cm and an inner diameter of 120 cm. What is the surface of the body, including the area inside the cavity?
• Rotary cylinder 2
  Base circumference of the rotary cylinder has same length as its height. What is the surface area of cylinder if its volume is 250 dm³?
• Rotary cylinder
  In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
• The coil
  How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
• Rotary cylinder
  The rotating cylinder has a surface area 69.08 cm². The area of the shell is 62.8 cm ². What is the diameter of the cylinder?
• Tin with oil
  Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm². Calculate how many liters of oil is in the tin.
• Cube volume
  The cube has a surface of 384 cm². Calculate its volume.