Circular pool

The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?

Correct result:

x =  6102 hl

Solution:

r=10 m t=10 m h=2 m a=t/2=10/2=5 m  α=2 arcsin(ar)=2 arcsin(510)1.0472 rad α2=α=α 180π=1.0472 180π=60  S1=π r2 2πα2π=3.1416 102 2 3.14161.04722 3.1416261.7994 m2  b=r2a2=10252=5 3 m8.6603 m  S2=a b2=5 8.6603221.6506 m2  S=S1+2 S2=261.7994+2 21.6506305.1007 m2  V=h S=2 305.1007610.2013 m3  x=V hl=V 10  hl=610.2013 10  hl=6102 hl



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
See also our right triangle calculator.
Do you know the volume and unit volume, and want to convert volume units?
See also our trigonometric triangle calculator.
Try conversion angle units angle degrees, minutes, seconds, radians, grads.

 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • Cylinder horizontally
    CylindricalSegment_1000 The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
  • Horizontal Cylindrical Segment
    cylinder_horiz How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
  • 9-gon pyramid
    9gon+Base+cone Calculate the volume and the surface of a nine-sided pyramid, the base of which can be inscribed with a circle with radius ρ = 7.2 cm and whose side edge s = 10.9 cm.
  • Pine wood
    dre-borovica From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lu
  • Children pool
    hexagon_prism2 The bottom of the children's pool is a regular hexagon with a = 60 cm side. The distance of opposing sides is 104 cm, the height of the pool is 45 cm. A) How many liters of water can fit into the pool? B) The pool is made of a double layer of plastic film
  • Circle arc
    pizza Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
  • Pool
    bazen Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 8 m, distance of the opposite walls of the pool is 7 m. Estimated depth is 144 cm. How many hectoliters of water consume Mr. Peter to fill the pool?
  • Circular segment
    odsek Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
  • Top of the tower
    veza The top of the tower has the shape of a regular hexagonal pyramid. The base edge has a length of 1.2 m, the pyramid height is 1.6 m. How many square meters of sheet metal is needed to cover the top of the tower if 15% extra sheet metal is needed for joint
  • Tent
    stan Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
  • Rotating cone
    kuzel_3 Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
  • Vintner
    wine How high can vintner fill keg with crushed red grapes if these grapes occupy a volume of 20 percent? Keg is cylindrical with a diameter of the base 1 m and a volume 9.42 hl. Start from the premise that says that fermentation will fill the keg (the number
  • Chocolate roll
    chocholate_3 The cube of 5 cm chocolate roll weighs 30 g. How many calories will contain the same chocolate roller of a prism shape with a length of 0.5 m whose cross section is an isosceles trapezoid with bases 25 and 13 cm and legs 10 cm. You know that 100 g of this
  • Maximum of volume
    kuzel2 The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
  • Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  • Canopy
    cone-roof Mr Peter has metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
  • Tetrahedral pyramid
    jehlan_1 Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm.