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?


S1 =  199.533 cm2
S2 =  208.199 cm2


V=180 h=15 V=πr2 h/3 r1=3 V/π/h=3 180/3.1416/153.3851 s=h2+r12=152+3.3851215.3772 S1=π r12+π r1 s=3.1416 3.38512+3.1416 3.3851 15.3772199.5326199.533 cm2V=180 \ \\ h=15 \ \\ V=\pi r^2 \ h / 3 \ \\ r_{1}=\sqrt{ 3 \cdot \ V/\pi/h }=\sqrt{ 3 \cdot \ 180/3.1416/15 } \doteq 3.3851 \ \\ s=\sqrt{ h^2+r_{1}^2 }=\sqrt{ 15^2+3.3851^2 } \doteq 15.3772 \ \\ S_{1}=\pi \cdot \ r_{1}^2+\pi \cdot \ r_{1} \cdot \ s=3.1416 \cdot \ 3.3851^2+3.1416 \cdot \ 3.3851 \cdot \ 15.3772 \doteq 199.5326 \doteq 199.533 \ \text{cm}^2
V=πr2 h r2=V/π/h=180/3.1416/151.9544 S2=2π r22+2π r2 h=2 3.1416 1.95442+2 3.1416 1.9544 15208.1988208.199 cm2V=\pi r^2 \ h \ \\ r_{2}=\sqrt{ V/\pi/h }=\sqrt{ 180/3.1416/15 } \doteq 1.9544 \ \\ S_{2}=2 \pi \cdot \ r_{2}^2+2 \pi \cdot \ r_{2} \cdot \ h=2 \cdot \ 3.1416 \cdot \ 1.9544^2+2 \cdot \ 3.1416 \cdot \ 1.9544 \cdot \ 15 \doteq 208.1988 \doteq 208.199 \ \text{cm}^2

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

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!

Tips to related online calculators
Tip: Our volume units converter will help you with the conversion of volume units.

Next similar math problems:

  1. Cone container
    kuzel_1 Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
  2. Rotary cylinder 2
    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?
  3. Cross-sections of a cone
    kuzel_rezy Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
  4. Truncated cone
    kuzel_komoly Calculate the height of the rotating truncated cone with volume V = 1115 cm3 and a base radii r1 = 7.9 cm and r2 = 9.7 cm.
  5. Cone area and side
    cone_2 Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
  6. Surface area
    cone_slice 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.
  7. Frustum of a cone
    cone-frustrum A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
  8. Sphere
    cone_sphere_center_1 Intersect between plane and a sphere is a circle with a radius of 60 mm. Cone whose base is this circle and whose apex is at the center of the sphere has a height of 34 mm. Calculate the surface area and volume of a sphere.
  9. 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.
  10. 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.
  11. Cylinder - A&V
    cylinder The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
  12. 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?
  13. Cylinder and its circumference
    cylinder If the height of a cylinder is 4 times its circumference c, what is the volume of the cylinder in terms of its circumference, c?
  14. 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.
  15. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  16. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  17. Coefficient
    gp Determine the coefficient of this sequence: 7.2; 2.4; 0.8