# Examples for 8th grade - page 4

- Square

Points A[-10,-1] and B[2,-1] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Chickens and rabbits

In the yard were chickens and rabbits. They had 28 heads and 82 legs. How many chickens and how many rabbits was in the yard? - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm^{2}. - Short cut

Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 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? - 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. - Gimli Glider

Aircraft Boeing 767 lose both engines at 44000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2000 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate - Discount

Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 70 USD. Determine the original price of sweater. - 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 cm^{2}. What scale is the city plan? - Rhombus

Calculate the perimeter and area of rhombus whose diagonals are 38 cm and 55 cm long. - Cube diagonal

Determine length of the cube diagonal with edge 33 km. - River

From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river. - Regular 5-gon

Calculate area of the regular pentagon with side 7 cm. - Logs

Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm? - Right triangle Alef

The area of a right triangle is 294 cm^{2}, the hypotenuse is 35 cm long. Determine the lengths of the legs. - Sphere

Surface of the sphere is 2820 cm^{2}, weight is 71 kg. What is its density? - Square and circles

Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles. - No. of divisors

How many different divisors has number ?? - Rectangle

In rectangle with sides 3 and 10 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? - Motion2

Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?

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