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:

$D=11 \ \text{m} \ \\ r=D/2=11/2=\dfrac{ 11 }{ 2 }=5.5 \ \text{m} \ \\ \ \\ S_{0}=4 \pi \cdot \ r^2=4 \cdot \ 3.1416 \cdot \ 5.5^2 \doteq 380.1327 \ \text{m}^2 \ \\ S=\dfrac{ 1 }{ 2 } \cdot \ 2 \cdot \ S_{0}=\dfrac{ 1 }{ 2 } \cdot \ 2 \cdot \ 380.1327 \doteq 380.1327 \ \text{m}^2 \ \\ \ \\ S_{1}=7.3 \ \text{m}^2 \ \\ \ \\ b=S/S_{1}=380.1327/7.3 \doteq 52.073 \doteq 52.073 \ \text{kg}$

$r_{1}=b=52.073 \ \text{dl} \ \\ r=r_{1} \rightarrow l=r_{1} / 10 \ l=5.2073 \ l=5.207 \ \text{l}$

Try another example

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

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Castle model
   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
   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
   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
   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
   The shop has 3 hectoliters of water. How many liter bottles is it?
6. Circular pool
   The 3.6-meter pool has a depth of 90 cm. How many liters of water is in the pool?
7. Hectoliters
   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
   Find the surface and volume of a sphere that has a radius of 2 dm.
9. 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?
10. Volume of ball
    Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π
11. Aquarium
    Aquarium is cube with edge 45 cm. How much water can fit in there?
12. Aquarium
    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
    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
    Find the surface of the cube that has volume 1/1m3 2/0.001 m³ 3/8000 mm³
15. Iron ball
    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
    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
    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