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.
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.
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.
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 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 m2. The first parcel is 40 m2 less than twice of the second one. What have acreage of each parcel?
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
Determine the resultant of two perpendicular forces F1 = 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 pulled a train permanent load of 200 kN horizontally along the track of 5km. What work it done?