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.

Correct answer:

V =  21189.6268 cm³

Step-by-step explanation:

$$\begin{gathered} S=4239{\text{cm}}^2 \\ D=h=2r \\ S=2\pi r^2+2\pi rh=2\pi r(r+h) \\ S=2\pi r(r+2r)=2\pi r3r=6\pi r^2 \\ r=\sqrt{{\displaystyle \frac{S}{6\pi }}}=\sqrt{{\displaystyle \frac{4239}{6\cdot 3.1416}}}\doteq 14.9962\text{ cm } \\ h=2\cdot r=2\cdot 14.9962\doteq 29.9924\text{ cm } \\ V=\pi \cdot r^2\cdot h=3.1416\cdot 14.9962^2\cdot 29.9924=21189.6268{\text{cm}}^3=2.119\cdot 10^4{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• 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.
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• Cylinder
  The cylinder surface is 922 dm². Its height is equal to the radius of the base. Calculate the height of this cylinder.
• Cube surface and volume
  The surface of the cube is 500 cm², how much cm³ will be its volume?
• Triangular prism
  The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface 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 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
• 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.
• Uboid volume
  Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
• Rhombus base
  Calculate the volume and surface area of prisms whose base is a rhombus with diagonals u₁ = 12 cm and u₂ = 15 cm. Prism height is twice the base edge length.
• Cube 6
  Volume of the cube is 216 cm³, calculate its surface area.
• Total area
  Calculate the total area (surface and bases) of a prism whose base is a rhombus which diagonals of 12cm and 18cm and prism height is 10 cm.
• Cube surfce2volume
  Calculate the volume of the cube if its surface is 150 cm².
• Area of a cube
  Calculate the surface area of a cube if its volume is equal to 729 cubic meters.
• Minimum surface
  Find the length, breadth, and height of the cuboid-shaped box with a minimum surface area, into which 50 cuboid-shaped blocks, each with length, breadth, and height equal to 4 cm, 3 cm, and 2 cm respectively, can be packed.
• Cylinder - h
  The cylinder volume is 140 cm³. The base radius is 7 cm. Calculate the height of the cylinder.
• Cylinder surface area
  Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm³. Calculate its surface area.