Examples for 9th grade - page 49
- The factory
The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3?
- Centre of mass
The vertices of triangle ABC are from the line p distances 3 cm, 4 cm and 8 cm. Calculate distance from the center of gravity of the triangle to line p.
- Outer contact of circles
Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contact. Calculate the perimeter of the triangle S1S2S3.
- Shoes and slippers
Shoes were three times as many as slippers. If shoes were cheaper by 120, it would be twice as expensive as slippers. How much cost shoes and how much slippers?
- Barrel 4
Barrel of water weighs 63 kg. After off 75% water, the weight of the barrel with water is 21 kg. How many kg weigh empty barrel and how many kgs water in it?
- Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
- Area of the cone
Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
Three scouts went on a three day trip. The second day went 4 km more than the first day. The third day went two times less than the first day. They went along 54 km. How many kilometers went every day together?
- Water well
Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?
- Circle inscribed
Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
- Field with vegetables
Field planted with vegetables has shape of a rectangular isosceles triangle with leg length of 24 m. At the vertices of the triangle are positioned rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated?
- Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 7 cm.
- Three co-owners
The three co-owners of building company have earnings from a contract portioned in the ratio of 3:6:7. Each of them received the amount in whole USD. One of them on contract earned 86450 USD. What was the total earnings this order?
- School year
At the end of the school year has awarded 20% of the 250 children who attend school. Awat got 18% boys and 23% of girls. Determine how many boys and how many girls attend school.
- The farmer
The farmer harvested 840 tons of grain in 2006, which was 44% less than in 2005, and one-fifth more than in 2004. How many tons of grain harvested in years 2005 and 2004?
- Uranium ore
Uranium ore contains 0.2% of pure uranium and pure uranium contains 0.07% of fissile uranium. How many grams of fissile uranium contains 2200 ton of uranium ore?
Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
- ISO triangle
Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 128 mm.