Examples for secondary school students
- Pyramid 4sides
Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm.
Solve algebrogram for sum of three numbers: BEK KEMR SOMR ________ HERCI
A 2 kg of apples cost a certain sum of money. This sum is equal to the amount of kilograms for which we pay 72 CZK. How much is 1 kg of apples?
- Support colum
Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m.
- 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.
- Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
- Roof 8
How many liters of air are under the roof of tower 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.
- 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 perimiter of the shaded figure is 75. Find the area of square ABCD
The pyramid has a base rectangle with a = 6cm, b = 8cm. The side edges are the same and their length = 12.5 cm. Calculate the surface of the pyramid.
- Cuboid and ratio
Cuboid has dimensions in ratio 1:2:6 and the surface area of the cuboid is 1000 dm2. Calculate the volume of the cuboid.
The rotating cone volume is 9.42 cm3, with a height 10 cm. What angle is between the side of the cone and its base?
- Hexagonal pyramid
Regular hexagonal pyramid has dimensions: 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.
- Potatoes bags
I have three bags with 21 kg potatoes. The first bag is 5.5 kg more than in the second bag and the third is 0.5 kg more than in the second bag. Determine how many kgs of potatoes is in each bag.
- Regular triangular prism
Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m.
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
- Alcohol mixture
From 55% and 80% alcohol we have to produce 0.2 kg of 60% alcohol. How many of them do we use in solution?
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
- Water reservoir
The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used.
- Sawmill factory
Peter works in the factory. The bus stop is 10 km from the factory. Therefore, always when the bus arrives for Peter, the driver leaves factory and takes him to work. They are coming at the saw exactly at 8:00. Today the bus arrived 11 minutes earlier and
- Water tank
The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?