Math practice for 13 year olds - page 203 of 413

Number of problems found: 8260

Train meeting calculation
When and where will two trains that run simultaneously from stations A and B at a distance of 60 km meet if the train from station A ran at 70 km/h and the train from station B at 50 km/h?
Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
Telegraph poles
The bases of two adjacent telegraph poles have a height difference of 10.5 m. How long do the wires connect the two poles if the slope is 39° 30’?
Surface of pyramid
A regular quadrilateral pyramid has the height of the sidewall equal to the length of the edge of the base. The area of the sidewall is 32 cm². What is the surface of the pyramid?
Calculate - prism
The base of the prism is a square with a side of 10 cm. Its height is 20 cm. Calculate the height of a pyramid with a square base of 10 cm, which has four times the prism's volume.
The observer - trees
The observer sees the tops of two trees at the same angle α. It is 9 m from one tree and 21 m from the other. The trees stand on a level. How tall is the second tree if the height of the first is 6 m? Remember that the eyes of a standing person are approx
Triangle height calculation
A parallelogram with a side length of 5 cm and a height to this side length of 4 cm has the same area as an isosceles triangle with a base length of 5 cm. What is the height of this triangle?
Prism pyramid volume
Calculate the body's volume, consisting of a prism and a pyramid with the same square base with an edge of 8 cm. The prism is 20 cm high, and the pyramid is 15 cm.
Electric work
Calculate the work done by the electric forces passing the current of 0.2 A through the bulb in 10 minutes if the bulb is connected to a 230 V power supply.
Two resistors
Two resistors, 20 Ω, and 60 Ω, are connected in series, and an external voltage of 400 V is connected to them. What are the electrical voltages on the respective resistors? Please comment!
Resistor series connection
Three resistors with resistances of 200 Ω, 400 Ω, and 600 Ω are connected in series (in series)—a current of 1.8 A flows through the first 200 Ω resistor. a) What current passes through the second and what current through the third resistor? b) What are t
Diamond area from diagonals
In the diamond, ABCD is AB = 4 dm, and the diagonal length is 6.4 dm long. What is the area of the diamond?
Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height?
Kirchhoff's law
Two resistors with 100 Ω and 300 Ω resistors are connected in series. A current of 1.8 A passes through the first 100 Ω resistor. What current flows through the second resistor?
Simultaneous start 2
A tourist who travels at a speed of 8 km in 2 hours and a cyclist who travels at a speed of 10 km in half an hour set off from two places 24 km apart simultaneously. How long are they on the road before they meet?
The rectangle
The rectangle has a circumference of 32 m. One side is 2 m longer than the other side. Calculate the side lengths of this rectangle.
Gutter pipe material
How much sheet metal do we use to produce a gutter pipe in the shape of a hollow half-cylinder 20 m long and 16 cm wide if we count 8% for bending and welding?
Triangle cone rotation
A thin plate in the shape of a right-angled triangle is turned once around the shorter hanger and a second time around the longer hanger. Cones are described by rotation. Are they the same volume? The dimensions are: shorter pendant 6 cm, longer pendant 8
Mains voltage
How much electric current flows through the appliance with a resistance of 40 kΩ, connected to the mains voltage (230 V)?
Resistor voltage
The current of 25 mA passes through the resistor with a resistance of 50 Ω. How much voltage do we measure on it?

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