# Square root - 8th grade (13y) - examples

- ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Garden

Area of square garden is 6/7 of triangle garden with sides 96 m, 60 m and 60 m. How many meters of fencing need to fence a square garden? - Pool

If water flows into the pool by two inlets, fill the whole for 9 hours. First inlet filled pool 8 hour longer than second. How long pool is filled with two inlets separately? - Cube in a sphere

The cube is inscribed in a sphere with volume 6598 cm^{3.}Determine the length of the edges of a cube. - Axial section

Axial section of the cone is equilateral triangle with area 300 m^{2.}Calculate volume of the cone. - Circle chord

What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm? - Rectangle

The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle. - Cuboid

The cuboid has a surface area 3380 cm^{2,}the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8? - Is right?

Is triangle with sides 24, 51 and 45 right triangle? - Square

Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 18 km/h, the second at average speed 24 km/h. Determine the distance between them after 30 minutes cycling. - Short cut

Imagine that you are going to the friend. That path has a length 330 meters. Then turn doprava and go another 840 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? - Scale

Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm^{2.}What scale is the city plan? - Cube diagonal

Determine length of the cube diagonal with edge 55 dm. - 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.} - 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. - 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?

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