# Unit conversion + area of shape - math problems

- Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm^{2}. What scale is the city plan? - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - Rainfall

Annual rainfall in our country are an average of 797 mm. How many m^{3}of water rains on average per hectare? - Area of trapezoid

The trapezoid bases are and 7 dm and 11 cm. His height is 4 cm. Calculate the area of trapezoid. - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube - 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? - Tetrahedral pyramid

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. - Windows

Calculate the area of masonry to build wall with dimensions of 9 m × 4 m with 4 windows of size 64 cm × 64 cm. - The pot

The pot is in 1/3 filled with water. Bottom of the pot has an area of 329 cm^{2}. How many centimeters rises water level in the pot after add 1.2 liters of water? - 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? - 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 m^{2}? - Plan of the village

Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality. - Rectangles

Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm? - Glass

At the glass shop we have to cut 8 sheets of glass. Each was shaped a square with sides of 18 cm. We paid 44 CZK. How much is a 1 m^{2}of glass? - Glass mosaic

How many dm^{2}glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%. - 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. - 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? - Vintner

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. - Diagonals in the diamond

The length of one diagonal in diamond is 24 cm greater than the length of the second diagonal and diamond area is 50 m^{2}. Determine the sizes of the diagonals. - Circle arc

Calculate the area of the circular arc in m^{2}where the diameter is 290 dm and a central angle is 135°. Result round to three decimal places.

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