# Grade - examples - page 82

- 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. - Cross-sections of a cone

Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body. - Tractor wheels

Smaller tractor wheel has a circumference of 3 meters, bigger 4 meters. On what path executes smaller wheel 6 turns over more bigger? - Pyramid in cube

In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid. - Every day 7 pages

Adelka reads the book every day 7 pages. When she reads one more page a day she will read it three days earlier. How long will Adelka read a book? How much does a book of pages have? - Pencils

Emil has 23 pencils in a pencil case, 18 of which were broken. Emily 9 trims, 2 breaks, 4 trims and goes to school. When he return from school, he has broken 5 pencils. How many pencils have trimed at school? - Cube corners

From cube of edge 14 cm cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will have this body? - Swimming pool

The pool shape of cuboid is 299 m^{3}full of water. Determine the dimensions of its bottom if water depth is 282 cm and one bottom dimension is 4.7 m greater than the second. - Sails

We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail? - Ratio - rectangle

The rectangle has dimensions 6 cm and 9 cm. How many times increases area and its perimeter, when its dimensions increase in the ratio 5:3? - Container with water

The weight of a container with water is 2.48 kg. If the cast 75% water, the container with water has a weight of 0.98 kg. Determine the weight of the empty container. How much water was originally in the container? - Cuboid - volume and areas

The cuboid has a volume of 250 cm^{3}, a surface of 250 cm^{2}and one side 5 cm long. How do I calculate the remaining sides? - Tiles

How many 46 cm square tiles will cover a floor 22.08 m by 8.74 m? - Triangle ABC

Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle a) rectangular b) acute-angled? - Water in aquarium

The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water. - Chess

How many different ways can initiate a game of chess (first pass)? - Bathroom

How many CZK we pay for lining the perimeter walls of the bathroom with rectangular shape with dimensions 3.5 m and 4 m, high 1.5 m if 1 square m tile cost 300 CZK? - Medians in triangle

Median of isosceles triangle has a length 3 cm. Determine the length of its sides if its perimeter is 16 cm. - Numbers

Find number on thenumber line that has same distance from this numbers: - Colors

Willie got birthday 6 colour pens in different colors. How many ways he can give them side by side in pencil?

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