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?

Result

S =  248.64 dm2

Solution:

h=2πr V=πr2h=πr22πr=2pi2r3=250 r=V2π23=2.33 dm h=2πr=14.65 dm  S=2πr2+2πrh=248.64 dm2h = 2\pi r \ \\ V = \pi r^2 h = \pi r^2 \cdot 2 \pi r = 2 \cdot pi^2 r^3 = 250 \ \\ r = \sqrt[3]{ \dfrac{V}{2\pi^2}} = 2.33 \ dm \ \\ h = 2 \pi r = 14.65 \ dm \ \\ \ \\ S = 2 \pi r ^2 + 2\pi r h = 248.64 \ dm^2







Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Following knowledge from mathematics are needed to solve this word math problem:

Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

  1. The cylinder base
    valec_4 The cylinder with a base of 8 dm2 has a volume of 120 liters. From a cylinder fully filled with water, 40 liters of water was removed. At what height from the bottom /with precision to dm/ is the water level?
  2. Cylinder surface, volume
    cyl 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.
  3. Volume and surface
    image001(1) 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.
  4. Cylinder surface area
    cylinder_2 Volume of a cylinder whose height is equal to the radius of the base is 678.5 dm3. Calculate its surface area.
  5. Jar
    sklenice From the cylinder shaped jar after tilting spilled water so that the bottom of the jar reaches the water level accurately into half of the base. Height of jar h = 7 cm and a jar diameter D is 12 cm. How to calculate how much water remains in the jar?
  6. Diameter of a cylinder
    cylinder I need to calculate the cylinder volume with a height of 50 cm and a diameter of 30 cm.
  7. A cylindrical tank
    tanks_8 A cylindrical tank can hold 44 cubic meters of water. If the radius of the tank is 3.5 meters, how high is the tank?
  8. Kitchen
    valcek_na_cesto Kitchen roller has a diameter 70 mm and width of 359 mm. How many square millimeters roll on one turn?
  9. Circular pool
    b1 The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
  10. Bottle
    cylinder_11 A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
  11. Surface of cuboid
    kvader11_9 Find the surface of the cuboid if its volume is 52.8 cm3 and the length of its two edges is 2 cm and 6 cm.
  12. Cuboid - Vab
    cuboid_3 Find the surface of the cuboid when its volume is 52.8 cubic centimeters, and the length of its two edges is 2 centimeters and 6 centimeters.
  13. Cuboid surface
    cuboid_4 Determine surface area of cuboid if its volume is 52.8 cm cubic and length of the two edges are 2 cm and 6 cm.
  14. Cube 1-2-3
    cube_shield_1 Calculate the volume and surface area of the cube ABCDEFGH if: a) /AB/ = 4 cm b) perimeter of wall ABCD is 22 cm c) the sum of the lengths of all edges of the cube is 30 cm.
  15. Spheres in sphere
    Spheres_in_sphere How many spheres with a radius of 15 cm can fits into the larger sphere with a radius of 150 cm?
  16. Cube walls
    cubes2_9 Find the volume and the surface area of the cube if the area of one of its walls is 40 cm2.
  17. Cuboid
    cuboid_12 Cuboid has a surface of 516 cm2. Side a = 6 cm and b = 12 cm. How long is the side c =?