# Examples for 9th grade - page 8

- Radians

Convert 270° to radians. Write result as multiple of number π. - Sea water

Mixing 62 kg of sea water with 84 kg rainwater is created water containing 3.1% salt. How many percent sea water contains salt? - Lathe

From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed? - Guests

How many ways can 9 guests sit down on 11 seats standing in a row? - 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? - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel. - Pedestrian up-down hill

Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian? - Diagonal

Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°. - Rotation

The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone. - Described

Calculate perimeter of the circle described by a triangle with sides 478, 255, 352. - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 21 cm and t_{b}=12 cm. - Kites

Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°? - Trapezoid

Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm.. - Tower

The top of the tower is a regular hexagonal pyramid with base edge 8 meters long and a height 5 meters. How many m^{2}of the sheet is required to cover the top of the tower if we count 8% of the sheet waste? - VAT

John paid 100 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%. - One half

One half of ? is: ? - R Trapezium

Rectangular trapezium has bases 12 and 5 and area 84 cm^{2}. What is its perimeter? - The cyclist

The cyclist went from village to town. First half of journey went at 20 km/h. The second half of the journey, which mostly fell, went at 39 km/h. All journey took 88 minutes. Calculate the distance from the village to the town. - 2nd class variations

From how many elements you can create 2450 variations of the second class? - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 33 and corresponding angle is ?.

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