Maths practice for 14 year olds - page 352 of 362
Number of problems found: 7232
- Radius
Determine the radius of a circle whose circumference and area are numerically equal. - Trapezoid
In a right-angled trapezoid, are the diagonals perpendicular to each other, and do they bisect the angles? - Motion
Cyclist started at 9:00 from point D to point E. After 10 minute, I followed him at the same speed as the second cyclist. Walker, which went from E to D, started at 9:25. After 40 minutes, he met the first cyclist and the second cyclist after the next 8 m - Proof PT
Can Pythagoras' theorem be easily proved using the Euclidean theorems? If so, do it. - Newton's task
Grass grows in the meadow equally fast and evenly. It is known that 35 cows graze meadow for 27 days and 39 cows by 24 days. How many cows graze the meadow for 6 days? - Divisors
Find all divisors of the number 553. How many are there? - Movement
Two cyclists set off from an intersection of two perpendicular roads, each taking a different road. One travels at an average speed of 16 km/h and the other at 25 km/h. Determine the distance between them after 20 minutes of cycling. - Wire D
A wire of length 6 m is bent to form the perimeter of a semicircle (including the diameter). Determine the radius of the semicircle. - Steps
How many steps do you save by walking diagonally across a square plot instead of walking along two of its sides, if the full perimeter takes 458 steps? - Estate
A semicircular plot of land is to be fenced. The straight section of the fence is 32 metres long. How many metres of fencing in total need to be bought? - Square 2
Points D[10,-8] and B[1,-10] are opposite vertices of square ABCD. Calculate the area of square ABCD. - Square
Points A[9,9] and B[-4,1] are adjacent vertices of square ABCD. Calculate the area of square ABCD. - Gimli Glider
A Boeing 767 loses both engines at an altitude of 35000 feet. The captain maintains optimal gliding conditions, losing 2100 feet per minute while maintaining a constant airspeed of 201 knots. Calculate how long it takes for the plane to reach the ground f - Triangle TBC
TBC is an isosceles triangle with base TB, base angle 75°, and equal legs |TC| = |BC| = 35. How long is the base TB? - Cubes
A sphere is inscribed in one cube and the same sphere is circumscribed about another cube. Calculate the difference between the volumes of the two cubes if the difference between their surface areas is 231 cm². - Forces
At point G, three mutually perpendicular forces act: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant force F and the angles between F and each of F₁, F₂, and F₃. - Diagonal
Determine the dimensions of a cuboid whose space diagonal is 60 dm and makes an angle of 35° with one edge and 77° with another edge. - Cone A2V
The lateral surface of a cone, when unrolled flat, forms a circular sector with a central angle of 126° and an area of 415 cm². Calculate the volume of the cone. - Axial section
The axial cross-section of a cone is an equilateral triangle with an area of 208 km². Calculate the volume of the cone. - Rotation
A right triangle with legs 11 cm and 18 cm is rotated around the longer leg. Calculate the volume and surface area of the cone formed.
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