Ratio - 9th grade (14y) - examples
On solving problems and tasks with proportionally we recommend hint rule of three. Rule of three (proportionality) help solve examples of direct and inverse proportionality. Three members makes possible to calculate the fourth - unknown member.
- The perimeter
The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
- Equilateral cylinder
A sphere is inserted into the rotating equilateral cylinder (touching the bases and the shell). Prove that the cylinder has both a volume and a surface half larger than an inscribed sphere.
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
Gross wage was 1430 USD including 23% bonus. How many USD were bonuses?
Route is long 147 km and the first day first regiment went at an average speed 12 km/h and journey back 21 km/h. The second day went second regiment same route at an average speed 22 km/h there and back. Which regiment will take route longer?
After three 10° beers consumed in a short time there are 5.1 g of alcohol in 5 kg adult human blood. How much is it per mille?
One meter of the textile were discounted by 2 USD. Now 9 m of textile cost as before 8 m. Calculate the old and new price of 1 m of the textile.
Calculate how many promiles river Vltava average falls, if on section long 928 km flowing water from 1592 m AMSL to 108 m AMSL.
Calculate how many average minutes a year is the web server is unavailable, the availability is 99.99%.
- Gimli Glider
Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1870 feet and maintain constant speed 212 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
- Eiffel Tower
Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 2.4 kg?
The areas of the two circles are in the ratio 2:14. The larger circle has diameter 14. Calculate the radius of the smaller circle.
Water pipe has a cross-section 1405 cm2. An hour has passed 756 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 15 hours if water flow same speed?
Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
Fields go plow two tractors with various performance. The first tractor plow whole field in 20 hours, the second tractor plow whole field 30 hours déle. How long take plow whole field with two tractors?
How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material.
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.
Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
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