# Square root - 9th grade (14y) - math problems

1. The tickets The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
2. Garden Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
3. Pool If water flows into the pool by two inlets, fill the whole for 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
4. TV transmitter The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
5. Cube in a sphere The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
6. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
7. Circle chord What is the length d of the chord circle of diameter 50 dm, if the distance from the center circle is 21 dm?
8. Rectangle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
9. Cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
10. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
11. Movement From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
12. Square Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
13. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
14. Rhombus Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
15. Short cut Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
16. Scale Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
17. Cube diagonal Determine the length of the cube diagonal with edge 75 mm.
18. Logs Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
19. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
20. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.

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