# Examples for 9th grade - page 56

- Rotating cone

Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm. - Rectangle

The length of the rectangle is 12 cm greater than 3 times its width. What dimensions and area this rectangle has if ts circumference is 104 cm. - Painting

The room is long 50 meters and wide 60dm and 300 cm high. Calculate how much it will cost painting if area of windows and doors is 15% of the total area. One square meter cost 50cents. - Concrete block

Determine the volume of concrete block whose one edge of the base has a length 3 meters, body diagonal is 13 meters and its height is 12 meters. - Inscribed circle

XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm. - Gravel - cone

Mound of gravel has shape of regular circular cone with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel are in the pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m. - Hexa prism

Determine the volume of hex prism with edge base 4 cm. The body height is 28 cm. - Mixing

If we mix 5 kg of goods of one kind and 3 kg second one, resulting mixture cost 16.50 EUR/kg. If these quantities are mixed in reverse - first three kilograms and 5 kilograms second cost of mixture is 18.50 EUR/kg. What is the price of one kg of goods of. - Float boya

A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/m - Passenger car and truck

From Kutna Hora left at 11:00 clock a truck at 60 km/h. At 12:30 behind him started passenger car at average speed 80 km/h. At what time and how far from Kutna Hora overtake a passenger car truck? - Rectangle - sides 4

Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5. - Three numbers

What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8. - Stairway

Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm. - Sum 10

What is the probability that two dice throw twice in a row will result the sum of 10? - Land areas

Two land areas is 244 m^{2.}The first parcel is 40 m^{2}less than twice of the second one. What have acreage of each parcel? - Tickets

On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)? - Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lum - Forces

Determine the resultant of two perpendicular forces F_{1}= 560 N and second force of 25% smaller. - Three numbers

Find three numbers so that the second number is 4 times greater than the first and the third is lower by 5 than the second number. Their sum is 67. - Locomotive

Locomotive pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done?

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