# Examples for secondary school students - page 3

1. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
2. Triangle SAS Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
3. Square Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
4. 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.
5. Discount Ladies sweater was twice discounted. First by 11%, then by 11% of the new price. Its final price was 100 €. Determine the original price of sweater.
6. Transforming cuboid Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
7. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
8. Gimli Glider Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes to plane from engine failure to hit the ground. Ca
9. River From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
10. Regular 5-gon Calculate area of the regular pentagon with side 7 cm.
11. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
12. Rectangle In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
13. No. of divisors How many different divisors have number ??
14. Square and circles Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
15. Proof PT Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
16. Observer The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
17. 7 heroes 9 heroes galloping on 9 horses behind. How many ways can sort them behind?
18. Pipes Water pipe has a cross-section 1087 cm2. An hour has passed 960 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 9 hours if water flow same speed?
19. Area of RT Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
20. Eiffel Tower Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 2.4 kg?

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