Math practice for 13 year olds - page 410 of 419
Number of problems found: 8372
- Pyramid roof
3/5 of the area of the roof-shaped regular tetrahedral pyramid with base edge 9 m and height of 6 m is already covered with roofing. How many square meters still need to be covered? - Cubes
Cube, which consists of 8 small cubes with edge 1 dm, has volume: - Right triangle
Right triangle ABC with side a = 10 and the area S = 50. Calculate the length of the remaining sides. - Square diagonal
Calculate the length of the diagonal of the square with side a = 11 cm. - Triangle
Can an equilateral triangle have a right angle? - Pool
The swimming pool is 10 m wide and 8 m long, and 153 cm deep. How many hectoliters of water are in it if the water is 30 cm below its upper edge? - Lines
Five bus lines run at intervals 4, 5, 7, 11, 12 minutes. In the morning, it suddenly starts at 7:00. After how many minutes do the bus lines meet again? - Numbers
Determine the number of all positive integers less than 5965074 if each is divisible by 5, 29, 11. What is its sum? - Circles
The areas of the two circles are in the ratio 5:10. The larger circle has a diameter of 14. Calculate the radius of the smaller circle. - Climb
The road has climbing 1:28. How big is the angle that corresponds to this climbing? - Pentagon
Calculate the area of a regular pentagon whose diagonal is u=18 long. - Compass
What angle is between directions J (Juh) and ZSZ (ZápadoSeveroZápad) on the compass? - Balance
The rod is 4.3 m long, hanging weights 9 kg and 15 kg on ends. Where is the center of the rod (distance from weight 9 kg) to be in balance? - Gear
Two gears fit into each other and have a transfer of 1:2. The centers of gears are spaced 96 cm. What are the radii of the gears? - Tinsmith
Tinsmith constructs chimney pipe 186 cm long and 16 cm wide. A pipe is made from the plate overlap at the joint and needs to add $x cm width of the plate. What dimensions of the sheet will have to be prepared for the construction? - Cubes
Surfaces of cubes, one of which has an edge of 42 cm shorter than the other, differ by 16128 cm². Determine the length of the edges of these cubes. - Free fall
Pavel fall from height 9 m. Calculate the speed at which he hit the ground when falling with acceleration g = 9.81 m/s² - Subway
The Subway train went between two stations that gradually accelerated for 26 seconds and reached a speed of 72 km/h. At this rate, it went 56 seconds. Then 16 seconds slowed to a stop. What was the distance between the stations? - Cuboid
Find the dimensions of cuboids a, b, and c; if diagonal d=6 dm has an angle with edge α=35° and has an angle with edge b β=66° - Cone
The circular cone has height h = 15 dm and base radius r = 2 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane if solids have the same volume.
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