Math practice for 13 year olds - page 201 of 424

Number of problems found: 8474

Quadrilateral prism
The surface of the regular quadrilateral prism is 8800 cm², and the base edge is 20 cm long. Calculate the volume of the prism
TV tower
Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°.
The ladder
The ladder touches a wall at the height of 7.5 m. The angle of the inclination of the ladder is 76°. How far is the lower end of the ladder from the wall?
Simultaneously 25481
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?
Insulating 25471
The septic tank is 6 m high and 2.4 m in diameter. If the painter consumes 1 kg per 5 m² and the paint is delivered in two kg cans, how many packages of insulating paint must he order?
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
Parallelogram 25371
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?
Calculate 25321
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!
Resistances 25271
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 200Ω resistor. a) What current passes through the second and what current through the third resistor? b) What are th
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 100Ω resistor. What current flows through the second resistor?
Simultaneously 25191
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.

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