Square root - 9th grade (14y) - examples
- Is right-angled
Can a triangle with the sides of sqrt 3, sqrt 5 and sqrt 8 (√3, √5 a √8) be a right triangle?
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 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 18 hours. First inlet filled pool 10 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 3724 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
- Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
Cuboid with edge a=24 cm and body diagonal u=50 cm has volume V=17280 cm3. Calculate the length of the other edges.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=10 and height v=18?
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 24 km/h, the second at average speed 16 km/h. Determine the distance between them after 35 minutes cycling.
Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
- 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?
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
- Cube diagonal
Determine length of the cube diagonal with edge 33 km.
Calculate the perimeter and area of rhombus whose diagonals are 2 cm and 6 cm long.
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
- Rhombus ABCD
Rhombus ABCD, |AC| = 97 cm, |BD| = 35 cm. Calculate the perimeter of the rhombus ABCD.
Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.