Square root - 9th grade (14y) - 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?
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?
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 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is equilateral triangle with area 300 m2. 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?
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=23 and height v=8?
Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
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?
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 13200 cm2. What scale is the city plan?
- Cube diagonal
Determine length of the cube diagonal with edge 55 dm.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm?
Calculate the perimeter and area of rhombus whose diagonals are 15 cm and 27 cm long.
Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
- Rhombus ABCD
Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD.
Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm.