Maths practice for 14 year olds - page 377 of 382
Number of problems found: 7628
- Track arc
Two straight railway tracks meet at an angle of 126°. They are joined by a circular arc with radius r = 1110 m. How long is the connecting arc (L)? How far is the centre of the arc from the intersection of the tracks (x)? - Seedcake
Seedcake costs 20 cents. How many minimum seedcakes must we buy that we can pay in cash, only whole euros? - Sphere slices
Calculate the volume and surface area of a sphere if two parallel circular cross-sections have radii r₁ = 32 cm and r₂ = 47 cm, and the distance between them is v = 21 cm. - Sphere cuts
At what distance from the centre does a plane intersect a sphere of radius R = 46, if the area of the circular cross-section and the area of the great circle are in the ratio 2:5? - Heron backlaw
Calculate the length of the unknown side of a triangle with sides 39 and 38 and area 438.6. - Triangle
Calculate all three altitudes of triangle ABC with sides a = 26, b = 81, and c = 73. - Diamond
Find the side length of a rhombus whose area is S = 194 cm² and one diagonal is u₂ = 44 cm. - Cone and cube
About what percentage has cone with base radius r larger volume than a same high cube with square base with edge length r? - The cap
A jester's hat is in the shape of a cone. Calculate how much paper is needed to make a hat 53 cm tall for a head circumference of 45 cm. - Cable car
A cable car rises at an angle of 44° and connects the upper and lower stations with an altitude difference of 1089 m. How long is the continuous (endless) tow rope? - Trigonometry
Given that cos(γ) = sin(806°), find the angle γ. - Steeple
A church tower is seen from the road at an elevation angle of 52°. When we move back a further 29 metres, it is seen at an elevation angle of 21°. How tall is the tower? - 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?
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