Maths practice for 14 year olds - page 149 of 361
Number of problems found: 7217
- Bracelet
The silver bracelet weighs 62 g and contains 59 g of silver. What is the purity of the bracelet? - Cone volume surface
A right triangle with perpendiculars a = 3 cm and b = 4 cm rotates around a longer perpendicular. Calculate the volume and surface area of the resulting cone. - Silver bracelet
The silver bracelet, which has a purity of 925 per mille, contains 25.9 g of silver. What is the weight of the bracelet? - Calculate
Calculate the height of an isosceles triangle with a base 37.8 mm long and an arm 23.1 mm long. - Ball probability
There are 6 white and several red balls in the box. How many red balls must there be so that the probability of drawing a red ball is less than the probability of drawing a white ball or greater than the probability of drawing a white ball? - 9-sided pyramid
Calculate the surface area and volume of a regular nine-sided pyramid if the radius of the circle inscribed in the base measures ρ = 12 cm and the height of the pyramid is 24 cm - Quadrilateral pyramid
In a regular quadrilateral pyramid, the length of the base edge is a = 8 cm, and the length of the side edge is h = 17 cm. Calculate the surface of the pyramid. - Hydraulic - piston
The large piston of the hydraulic system has a capacity of 0.25 m² and a small 10 cm². How much force do we exert on the small piston to be lifted by 750 N? - Hydraulic blade force The hydraulic blade has pistons with an area of 10 cm² and 500 cm². How much force acts on the larger piston if we act on the smaller piston with a force of 100 N?
- Hydraulic jack The small piston of the hydraulic jack has a capacity of 40 cm² and a large 120 cm². How heavy will a body lift when a man weighing 70 kg stands on a small piston?
- Electric cooker
During which time does an electric cooker with power input P = 500 W and efficiency n = 75% heat water with mass m = 2 kg and temperature t1 = 10 °C to the boiling point (t2 = 100 °C)? The specific heat capacity of water is c = 4 180 J/kg/K. - System equation solving
Solve the following system of equations: x + 4y = 5 2x - 3y = -6 - Sphere cube filling
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill? - Roof height
Calculate the height of the house's roof, which is an isosceles triangle with a base of 8.4 m and arms of 6.5 m. - Cake portion comparison
Three children got part of the cake. Which got the most? Tomas 24% Lenka 0.3 Philip 2/7 - Surface area and volume
Find the surface area and volume of a rotating cone whose diameter is 60 mm and side length is 3.4 cm. - Product selection ways
Among the 24 products, seven are defective. How many ways can we choose to check a) 7 products so that they are all good b) 7 products so that they are all defective c) 3 good and two defective products? - A license
A licence plate has three letters followed by four digits. Letters may not be repeated, but digits may be repeated. If plates are issued at random, what is the probability that the three letters are in alphabetical order and the four digits are consecutiv - School parliament
There are 18 boys and 14 girls in the class. In how many ways can three representatives be elected to the school parliament if these are to be: a) the boys themselves b) one boy and two girls - Total area
Calculate the total area (surface and bases) of a prism whose base is a rhombus with 12 cm and 18 cm diagonals and whose prism height is 10 cm.
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