Maths practice for 14 year olds - page 145 of 375

Number of problems found: 7494

Right triangle
A circle with a radius of 5 cm is described in a right triangle with a 6 cm leg. What is the height at the hypotenuse of this triangle?
Candy distribution
Adela and Barbora have a total of 34 candies. If Barbora gives Adela 2 candies, they will have the same. How many candies does Adela have, and how many Barbora?
Original price
Find the original price of a car if it was firstly increased by 4% and then reduced by 2%. It now costs CZK 326,144.
Truck kinetic energy
The truck weighs 4.5 tons and is moving at a constant speed of 72 km/h. How big is his kinetic energy?
Box wrapping cost
How much will we pay for wrapping 5 boxes in the shape of a cube with a side length of 80 cm if we count on a margin of 35% for folds? The price for 1 square meter of paper is €2.55. You can only buy whole square meters.
The cone - S,V
Calculate the volume and surface area of the cone if its radius r = 6 cm and side s = 10 cm.
Bracelet
The silver bracelet weighs 62g and contains 59g 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.
Triangle right determination
Decide if the triangle is right (sides 5,11,7, cm)
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?

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