# Examples for 9th grade - page 63

- Wall diagonal

Calculate the length of wall diagonal of the cube whose surface is 384 cm square. - Cuboid enlargement

By how many percent increases the volume of cuboid if its every dimension increases by 30%? - Tetrahedral prism - rhomboid base

Calculate the area and volume tetrahedral prism that has base rhomboid shape and its dimensions are: a = 12 cm, b = 70 mm, v_a = 6 cm, v_h = 1 dm. - Three friends

Danica, Lenka and Dalibor have altogether 96 kg. Lenka weighs 75% more than Dalibor and Danica weighs 6 kg more than Dalibor. Determine the weight of Danice, Lenka and Dalibor. - Vegan shop

To the shops brought together 23.2 kg of goods, fruits, vegetables and nuts. fruit was 4.7 kg more than vegetables, nuts was 1.5 kg less than the fruit. Determine the amount of fruits, vegetables and nuts. - Quotient

Determine the quotient and the second member of the geometric progression where a3=10, a1+a2=-1,6 a1-a2=2,4. - Threesome

Dana, Dalibor and Michael have a combined 57 years. Dana is five years older than Dalibor, but Dana is five years younger than Michael. Determine how old is Dana, Dalibor and Michael. - Divisibility

Write all the integers x divisible by seven and eight at the same time for which the following applies: 100 - Remuneration

Total remuneration for workers is 47 000 CZK. The second worker received 20% more than the first and third 4000 CZK less than a second employee. How many CZK each received? - The field

The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters. - Summerjob

Three students participated in the summerjob. Altogether they earn 1780, -. Peter got a third less than John and Paul got 100,- more than Peter. How much got every one of them? - 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. - 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 - 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. - Copper plate

Calculate the thickness of the copper plate with a density 8.7 g/cm³ measuring 1.5 meters and 80 cm and its weight is 3.65 kg - Octahedron

All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron. - Three piles

100 kg of sugar we divide into three piles. The first pile is small. If we added to second 2 kg of sugar it would have 25% more sugar than the first pile. If we added to third pile 3 kg of sugar it would have 20% more sugar than the 2nd pile. How many kil - Lamp cone

Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 cm. - Ascent and descent

Car goes 114 km track, which consists of ascent and descent at time of 1 hour 35 minutes. When climbing moves at the speed 48 km/h and downhill 25 m/s. What is the length of climb and descent? - Perimeter of circle

Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.

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