Cylinder diameter

The surface of the cylinder is 149 cm². The cylinder height is 6 cm. What is the diameter of this cylinder?

Correct answer:

D =  5.439 cm

Step-by-step explanation:

$$\begin{gathered} S=2\pi r^2+2\pi rh \\ S=\pi D^2\mathrm{/}2+\pi Dh \\ \pi D^2\mathrm{/}2+\pi Dh-S=0 \\ \pi D^2\mathrm{/}2+\pi \cdot 6\cdot D-149=0 \\ 1.5707963267949D^2+18.85D-149=0 \\ a=1.5707963267949;b=18.85;c=-149 \\ D=b^2-4ac=18.85^2-4\cdot 1.5707963267949\cdot (-149)=1291.500369209 \\ D>0 \\ {D}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{-18.85\pm \sqrt{1291.5}}{3.1415926535898}} \\ {D}_{1,2}=-6\pm 11.43924587037 \\ {D}_1=5.4392458703697 \\ {D}_2=-17.43924587037 \\ \text{ Factored form of the equation: } \\ 1.5707963267949(D-5.4392458703697)(D+17.43924587037)=0 \\ D>0 \\ D\doteq 5.439\text{ cm} \end{gathered}$$

Try another example

Related math problems and questions:

• 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?
• 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.
• 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.
• The surface
  The surface of the cylinder is 1570 cm², its height is 15 cm. Find its volume and radius of the base.
• Equilateral cylinder
  Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm³ . Calculate the surface area of the cylinder.
• Hexagonal prism 2
  The regular hexagonal prism has a surface of 140 cm² and height of 5 cm. Calculate its volume.
• 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.
• Rotary cylinder
  In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height.
• 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?
• 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
• Closed drum
  Find the total surface area of a closed cylindrical drum if it's diameter is 50 cm and height is 45 cm. (π= 3.14)
• 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.
• Tank
  In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
• Cuboid and eq2
  Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm².
• Cylinder - h
  The cylinder volume is 140 cm³. The base radius is 7 cm. Calculate the height of the cylinder.
• 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.
• Solid cuboid
  A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig.