# Examples for 8th grade - page 4

- Cube diagonal

Determine length of the cube diagonal with edge 55 dm. - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2.}Calculate the volume of a cone. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm^{2.} - Discount

Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 72 USD. Determine the original price of sweater. - Regular 5-gon

Calculate area of the regular pentagon with side 11 cm. - Logs

Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm? - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 15 cm and 27 cm long. - Right triangle Alef

The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs. - Square and circles

Square with sides 89 m is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Sphere

Surface of the sphere is 2260 cm^{2,}weight is 52.2 kg. What is its density? - Motion2

Cyclist started out of town at 20 km/h. After 0.6 hours car started behind him in the same direction and caught up with him for 52 minutes. How fast and how long went car from the city to caught cyclist? - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - ŽSR

Calculate fixed annual personnel costs of operating monorail line 106 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 3-shift operation. Consider the average salary of the employee 847 €. - No. of divisors

How many different divisors has number ?? - Rectangle

In rectangle with sides 10 and 9 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? - Rhombus ABCD

Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD. - Diagonal

Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm. - Area of RT

Calculate the area of a right triangle which hypotenuse has length 20 and one hypotenuse segment has lenght 15. - Two cars

Two cars started against each other at the same time to journey long 225 km. First car went 35 km/h and second 48 km/h. What distance will be between this cars 20 minutes before meet? - Circles

The areas of the two circles are in the ratio 1:15. The larger circle has diameter 25. Calculate the radius of the smaller circle.

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