Maths practice for 14 year olds - page 290 of 362

Number of problems found: 7230

Roof 8
How many liters of air is under the tower's roof, which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
Apples
A 2 kg of apples cost a certain sum of money. This sum equals the number of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
Vase capacity
The cylindrical vase is 28 cm high. Its inner diameter d = 1.1 dm. How many liters of water will fit in it if the bottom thickness is 1.5 cm?
Water height
The cylindrical container with a diameter of 1.8 m contains 2000 l of water. What height does the water reach?
Rotating cone
Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
Algebrogram
Solve cryptarithmetic (alphametics) for a sum of three numbers: BEK KEMR SOMR ________ HERCI
Pyramid
The pyramid has a base rectangle with a = 6 cm and b = 8 cm. The side edges are the same, and their length is 12.5 cm. Calculate the surface of the pyramid.
Two numbers
The sum of the two numbers is 75. Find these numbers. Three-quarters of the first are one-seventh of the second.
Polygon angle
A regular 15-angle is given. A triangle is formed if we connect points 3 and 7, 13 and 10. The vertices are 3 and 13, and the lines' intersections are 3.7 and 13.10. We are to determine the angle size formed by sides 3.7 and 13.10. These numbers indicate
Hectoliters in a tank
The block tank held 288 hectoliters of water. The bottom dimensions are 12m and 6m, and the depth is 2m. What percent of the tank volume does the water occupy?
Larger number
Which number a is 15 smaller (solve also for a is larger) than its half?
Hexagonal prism height
A container has the shape of a regular hexagonal prism with a base and a capacity of 0.5 dm², which means three quarter-liter cups of water fill the brim. What is the height of a container?
Cuboid and ratio
A cuboid has dimensions in a ratio of 1:2:6, and the surface area of the cuboid is 1000 dm². Calculate the volume of the cuboid.
Cone
The rotating cone volume is 9.42 cm³, with a height of 10 cm. What angle is between the side of the cone and its base?
The road
The road roller has a diameter of 1.2 m and a width of 180 cm. How many m² of the road does it level when it turns 35 times?
Folded square
ABCD is a square. The square is folded on the midpoint of AB, and A is folded onto the fold, creating a shaded region. The perimeter of the shaded figure is 75. Find the area of square ABCD
Money distribution
Pavol, Edita and Juraj have a total of 1243 euros. Pavol has 200 euros more than Edita, Juraj has 457 euros less than Edita. Determine how much each has.
Mother and son age
The son and mother are 32 years old together. My mother is 28 years older. Find how old they are.
Hexagonal pyramid
A regular hexagonal pyramid has dimensions: the length edge of the base a = 1.8 dm, and the height of the pyramid = 2.4 dm. Calculate the surface area and volume of a pyramid.
Cone surface
Calculate the surface and volume of the rotating cone, whose base circumference is 125.6 cm and the side is 25 cm long.

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