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.

Correct answer:

S =  452.352 dm²

Step-by-step explanation:

$$\begin{gathered} V=678.5 \\ h=r \\ V=\pi r^{2}h=\pi r^3 \\ r=\sqrt[3]{V\mathrm{/}\pi }=\sqrt[3]{678.5\mathrm{/}3.1416}\doteq 5.9998 \\ h=r=5.9998\doteq 5.9998 \\ S=2\pi \cdot r^2+2\pi \cdot r\cdot h=2\cdot 3.1416\cdot 5.9998^2+2\cdot 3.1416\cdot 5.9998\cdot 5.9998=452.352{\text{dm}}^2 \end{gathered}$$

Try another example

Related math problems and questions:

• Cylinder
  The cylinder surface is 922 dm². Its height is equal to the radius of the base. Calculate the height of this cylinder.
• 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.
• 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.
• 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?
• Surface and volume
  Calculate the surface and volume of a cylinder whose height is 8 dm and the radius of the base circle is 2 dm  
• 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.
• Cylinder - basics
  Cylinder with base radius r = 54 cm and height h=35 cm. Calculate: a) Area of the base
• Cylinder - A&V
  The cylinder has a volume 1287. The base has a radius 10. What is the area of the surface of the cylinder?
• The cylinder 2
  Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
• Cylinder height
  Calculate the height of the cylinder and its surface is 2500 dm² and the bases have a diameter 5dm.
• 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.
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• The volume
  The volume of the cone is 94.2dm³, the radius of the base is 6 dm Calculate the surface of the cone.
• 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?
• Rotating cone
  Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
• 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.
• Cylinder - area
  The diameter of the cylinder is one-third the length of the height of the cylinder. Calculate the surface of cylinder if its volume is 2 m³.