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.

Correct answer:

V =  596.831 cm³

Step-by-step explanation:

$$\begin{gathered} S=300{\text{cm}}^2 \\ h=12\text{ cm } \\ S=2\pi \cdot r\cdot h \\ r={\displaystyle \frac{S}{2\pi \cdot h}}={\displaystyle \frac{300}{2\cdot 3.1416\cdot 12}}\doteq 3.9789\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3.9789^2\doteq 49.7359{\text{cm}}^2 \\ V=S_1\cdot h=49.7359\cdot 12=596.831{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• The cylinder
  The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder.
• 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.
• Surface of the cylinder
  Calculate the surface of the cylinder for which the shell area is Spl = 20 cm² and the height v = 3.5 cm
• Diameter = height
  The cylinder's surface, the height of which is equal to the diameter of the base, is 4239 cm square. Calculate the cylinder volume.
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The prism base is a rhombus with a side length of 30 cm and a height of 27 cm. The height of t
• Rotary cylinder
  In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• What is
  What is the height of a cylinder whose surface size is 602.88 cm² and the content of its shell is 376.8 cm²?
• 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.
• Surface area
  The volume of a cone is 1000 cm³ and the content area of the axis cut is 100 cm². Calculate the surface area of the cone.
• Hexagonal prism 2
  The regular hexagonal prism has a surface of 140 cm² and height of 5 cm. Calculate its volume.
• Height as diameter of base
  The rotary cylinder has a height equal to the base diameter and a surface of 471 cm². Calculate the volume of a cylinder.
• Cylinder - h
  The cylinder volume is 140 cm³. The base radius is 7 cm. Calculate the height of the cylinder.
• Cuboid and eq2
  Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm².
• Cylinder
  The cylinder surface is 922 dm². Its height is equal to the radius of the base. Calculate the height of this cylinder.
• Cuboid walls
  Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm².
• 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?