# Examples for 8th grade - page 31

- Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Paul and Honza

Honza went to chat on a bike without a break 3.0 hours. Paul the same way without breaks 30 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not. - Gasholder

The gasholder has spherical shape with a diameter 23 m. How many m^{3}can hold in? - Invitations

For every 5 minutes writes Dana 10 invitations, while Anna 14 invitations. How long will write together 120 invitations? - Cuboids in cube

How many cuboids with dimensions of 6 cm, 8 cm and 12 cm can fit into a cube with side 96 centimeters? - Squaring the Circle

Calculating side of the square with the same area as the circle of radius 18. - Mountain railway

Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track. - Jan

Jan is 13 years and Peter 21 years old. For how many years will their ages in the ratio of 7:9? - Swing

A child weighing 12 kg is sitting on a swing at a distance of 130 cm from the axis of rotation. How far away from the axis of rotation (center) must sit down his mother weighs 57 kg if she wants to be swing in balance? - Again saw

From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 128 mm and 140 mm. What is the trunk smallest diameter? - Pennies

800 pennies have the same value as 100 ducats. 100 pennies have the same value as 250 tolars. How many ducats has the same value as 100 tolars? - Two workers

Two workers carry will do certain work for 12 days. After 8 days of working was one removed, and then the other finished the job alone in 10 days. For how many days would do this work alone each worker? - Train from Brno

First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers. - ISO trapezoid v2

bases of Isosceles trapezoid measured 12 cm and 2 cm and its perimeter is 18 cm. What is the are of a trapezoid? - Words

How many 3 letter "words" are possible using 18 letters of the alphabet? a) n - without repetition b) m - with repetition - Chalet

The children were on a school trip to the mountain . One third of the journey went by the train and continue by bus. When you get off the bus, they remained a third of the distance they traveled by bus. What part of journey children went by the bus (wrote - Tournament

Determine how many ways can be chosen four representatives from 27 students to school tournament. - Hexagonal prism

The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism! - Swimming pool 4

The pool shaped cuboid measuring 12.5 m × 640 cm at the bottom is 960hl water. To what height in meters reaches the water level? - Reflector

Circular reflector throws light cone with a vertex angle 60° and is on 22 m height tower. The axis of the light beam has with the axis of the tower angle 24°. What is the maximum length of the illuminated horizontal plane?

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