Square root - 8th grade (13y) - math problems
- The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets, as well as their product, was the power of the prime number. Find all possible ticket prices.
Area of a 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 8 hours. The first inlet filled pool 6 hour longer than second. How long pool take to fill with two inlets separately?
- Cube in a sphere
The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
- Circle chord
What is the length d of the chord circle of diameter 50 dm, if the distance from the center circle is 21 dm?
The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
- Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
- Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling.
Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
- Is right?
Is triangle with sides 51, 56 and 77 right triangle?
Calculate the perimeter and area of a rhombus whose diagonals are 38 cm and 55 cm long.
- Short cut
Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 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 8.25 cm2. What scale is the city plan?
- Cube diagonal
Determine the length of the cube diagonal with edge 75 mm.
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
- Square and circles
Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.