Children pool

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. How many m² of foil do you need to make one pool?

Correct result:

V =  421.2 l
S =  5.112 m²

Solution:

$$\begin{gathered} a=60\mathrm{/}10=6\text{ dm } \\ x=104\mathrm{/}10={\displaystyle \frac{52}{5}}=10.4\text{ dm } \\ h=45\mathrm{/}10={\displaystyle \frac{9}{2}}=4.5\text{ dm } \\ v=x\mathrm{/}2=10.4\mathrm{/}2={\displaystyle \frac{26}{5}}=5.2 \\ {S}_1=a\cdot v\mathrm{/}2=6\cdot 5.2\mathrm{/}2={\displaystyle \frac{78}{5}}=15.6{\text{dm}}^2 \\ {S}_6=6\cdot S_1=6\cdot 15.6={\displaystyle \frac{468}{5}}=93.6{\text{dm}}^2 \\ V=S_6\cdot h=93.6\cdot 4.5={\displaystyle \frac{2106}{5}}={\displaystyle \frac{2106}{5}}\text{ l}=421.2\text{ l} \end{gathered}$$

$$\begin{gathered} o=6\cdot a=6\cdot 6=36\text{ dm } \\ S=2\cdot (S_6+o\cdot h)\mathrm{/}100=2\cdot (93.6+36\cdot 4.5)\mathrm{/}100={\displaystyle \frac{639}{125}}={\displaystyle \frac{639}{125}}{\text{m}}^2=5.112{\text{m}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Next similar math problems:

• Top of the tower
  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
• Hexagonal prism
  The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Find the volume and surface of the prism.
• Four prisms
  Question No. 1: The prism has the dimensions a = 2.5 cm, b = 100 mm, c = 12 cm. What is its volume? a) 3000 cm² b) 300 cm² c) 3000 cm³ d) 300 cm³ Question No.2: The base of the prism is a rhombus with a side length of 30 cm and a height of 27 cm. The heig
• 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?
• Dusan
  a) Dusan break two same window, which has triangular shape with a length of 0.8 m and corresponding height 9.5 dm. Find how many dm² of glass he needs to buy for glazing of these windows. b) Since the money to fix Dusan has not, must go to the paint job
• Roof 8
  How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
• Aquarium
  The box-shaped aquarium is 40 cm high; the bottom has dimensions of 70 cm and 50 cm. Simon wanted to create an exciting environment for the fish, so he fixed three pillars to the bottom. They all have the shape of a cuboid with a square base. The base edg
• Pool
  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?
• Children's pool
  Children's pool at the swimming pool is 10m long, 5m wide and 50cm deep. Calculate: (a) how many m² of tiles are needed for lining the perimeter walls of the pool? (b) how many hectoliters of water will fit into the pool?
• Tent
  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.
• Canopy
  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?
• Cone
  Circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
• Truncated pyramid
  How many cubic meters is volume of a regular four-side truncated pyramid with edges one meter and 60 cm and high 250 mm?
• The tent
  The tent shape of a regular quadrilateral pyramid has a base edge length a = 2 m and a height v = 1.8 m. How many m² of cloth we need to make the tent if we have to add 7% of the seams? How many m³ of air will be in the tent?
• Hexagonal pyramid
  Regular hexagonal pyramid has dimensions: length edge of the base a = 1.8 dm and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
• Prism 4 sides
  The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
• Cylinder horizontally
  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?