# Examples for 9th grade - page 7

- Cyclist

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? - Right triangle

Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle. - Spherical cap

From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere? - Pentagon

Calculate the area of regular pentagon, which diagonal is u=17. - Mast

Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Sea water

Seawater contains about 4.3% salt. How many dm^{3}of distilled water we must pour into 5 dm^{3}of sea water to get water with 1.8% salt? - Climb in percentage

The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km. - Road repair

Road repair took 10 days for 36 workers if they worked 9 hours a day. How many days take repair same road 37 workers if they work 8 per day? - Pediatrician

Pediatrician this month of 19 working days takes 3 days holidays. What is the probability that on Monday will be at work? - Barrel of oil

Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel? - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Engineer Kažimír

The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri - Cube zoom

How many percent we increase volume and surface of cube, if we magnify its edge by 38%. - Rectangle - sides ratio

Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673. - Rhombus and inscribed circle

It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals. - Car

Car goes from point A to point B at speed 86 km/h and back 53 km/h. If they goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is distance between points A and B? - Maximum area of rhombus

Calculate the interior angles at which equilateral rhombus has maximum area. - Gear

Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears? - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm.

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