Hemisphere - roof

The shape of the observatory dome is close to the hemisphere. Its outer diameter is 11 m. How many kilograms of paint and how many liters of paint is used for its double coat if you know that 1 kg of paint diluted with 1 deciliter of paint will paint an area of 7.3 dm2.

Result

b =  52.073 kg
r =  5.207 l

Solution:

D=11 m r=D/2=11/2=112=5.5 m  S0=4π r2=4 3.1416 5.52380.1327 m2 S=12 2 S0=12 2 380.1327380.1327 m2  S1=7.3 m2  b=S/S1=380.1327/7.352.07352.073 kgD=11 \ \text{m} \ \\ r=D/2=11/2=\dfrac{ 11 }{ 2 }=5.5 \ \text{m} \ \\ \ \\ S_{0}=4 \pi \cdot \ r^2=4 \cdot \ 3.1416 \cdot \ 5.5^2 \doteq 380.1327 \ \text{m}^2 \ \\ S=\dfrac{ 1 }{ 2 } \cdot \ 2 \cdot \ S_{0}=\dfrac{ 1 }{ 2 } \cdot \ 2 \cdot \ 380.1327 \doteq 380.1327 \ \text{m}^2 \ \\ \ \\ S_{1}=7.3 \ \text{m}^2 \ \\ \ \\ b=S/S_{1}=380.1327/7.3 \doteq 52.073 \doteq 52.073 \ \text{kg}
r1=b=52.073 dl r=r1l=r1/10 l=5.2073 l=5.207 lr_{1}=b=52.073 \ \text{dl} \ \\ r=r_{1} \rightarrow l=r_{1} / 10 \ l=5.2073 \ l=5.207 \ \text{l}



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!
avatar




Tips to related online calculators
Do you know the volume and unit volume, and want to convert volume units?

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

Next similar math problems:

  1. Castle model
    kuzel2 The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm2 of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of wo
  2. Hemispherical hollow
    odsek The vessel hemispherical hollow is filled with water to a height of 10 cm =. How many liters of water are inside if the inside diameter of the hollow is d = 28cm?
  3. 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?
  4. Cylindrical tank 2
    watertank_3 If a cylindrical tank with volume is used 12320cm raised to the power of 3 and base 28cm is used to store water. How many liters of water can it hold?
  5. The shop
    lahev The shop has 3 hectoliters of water. How many liter bottles is it?
  6. Circular pool
    b1 The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
  7. Hectoliters
    hl How many hectoliters of water fits into cuboid tank with dimensions of a = 3.5 m b = 2.5 m c = 1.4 m?
  8. Sphere VS
    gule Find the surface and volume of a sphere that has a radius of 2 dm.
  9. 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?
  10. Volume of ball
    ball1_5 Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
  11. Aquarium
    akvarko Aquarium is cube with edge 45 cm. How much water can fit in there?
  12. Aquarium
    akvarium Aquarium is rectangular box with square base containing 76 liters of water. Length of base edge is 42 cm. To what height the water level goes?
  13. Spherical tank
    spherical-tanks The tank of a water tower is a sphere of radius 35ft. If the tank is filled to one quarter of full, what is the height of the water?
  14. Surface of the cube
    cubes3 Find the surface of the cube that has volume 1/1m3 2/0.001 m3 3/8000 mm3
  15. Iron ball
    damper_sphere The iron ball has a weight of 100 kilograms. Calculate the volume, radius, and surface if the iron's density is h = 7.6g/cm3.
  16. Spherical segment
    circular_segment_1 Spherical segment with height h=7 has a volume V=198. Calculate the radius of the sphere of which is cut this segment.
  17. Volume of the cone
    kuzel Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm