Maths practice for 14 year olds - page 357 of 361

Number of problems found: 7215

Glass of juice
A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling.
Chord MN
Chord MN of a circle has a distance of 28 cm from the centre S. Angle MSN is 54°. Determine the radius of the circle.
Circle
A circle k has diameter |MN| = 85. Point J lies on circle k. If |NJ| = 12, calculate the length of segment JM.
Median
In triangle NOP, the centroid is 95 cm from vertex P. Calculate the length of the median from vertex P.
Black building
Jozef built a building with a rectangular footprint of 3.9 m × 6.7 m. Calculate by what percentage the building exceeds the legal limit of 25 m² for a small building. A building constructed without planning permission is called an illegal building. Also c
Event probability
The probability of event N in 5 independent experiments is 0.4. What is the probability that the event N occurs in one experiment (chance is the same)?
Shooter
The probability that a skilled shooter hits the centre of target zone I is 0.13. The probability of hitting inner circle II is 0.58. What is the probability that the shooter hits zone I or zone II?
Flags
How many different flags can be made from green, white, blue, red, orange, yellow, and purple materials if each flag consists of three stripes of different colours?
Loans, loan ...
Short-term non-bank loans in Slovakia are considered very unfavourable. Borrowers often end up in a debt spiral, taking out increasingly burdensome loans to repay earlier ones. Calculate how many 7-year loans of €1400 at 23% APR a person can repay if thei
Right triangle
The legs of a right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 810 cm.
Barrel of oil
The barrel of oil weighs 283 kg. When it molded 26% oil, it weighed 216 kg. What is the mass of the empty barrel?
Golden ratio
Divide the line of length 871 cm into two sections so that the ratio of shorter to greater is the same as the ratio of the greater section to the whole length of the line.
Magnification of the square
If the side of a square is increased, the area increases by 57%. By what percentage was the side increased?
The cyclist
A cyclist travelled from a village to a town. The first half of the journey was at 24 km/h. The second half, which was mostly downhill, was at 38 km/h. The entire journey took 94 minutes. Calculate the distance from the village to the town.
Circle and angle
What is the arc length of a circle with radius r = 432 dm corresponding to a central angle of 0.53 rad?
Widescreen monitor
Widescreen monitors and televisions have flooded the market. Calculate the screen area of an LCD monitor with a diagonal of 27 inches at a 4:3 aspect ratio and then at a 16:9 aspect ratio. Is buying a widescreen monitor with the same diagonal more advanta
Roller
The lateral surface area of a cylinder equals the area of one of its bases. The cylinder height is 23 dm. What is the radius of the base of the cylinder?
Cylinder - basics
A cylinder has a base radius r = 24 cm and height h = 62 cm. Calculate: a) The area of the base
Cylinder - A&V
A cylinder has a volume of 463. Its base has a radius of 4. What is the total surface area of the cylinder?

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