Examples for 9th grade - page 16
- 3y inflation
Price of the bread rise in the first year by 7%, the second year fell by 4% and in the third year increased by 8%. Calculate the average annual increase in price of the bread.
- Cardboard box
We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal
What is the weight of concrete cover (lid) to round shape well with a diameter 1.3 m, if the thickness of the cover is 15 cm? 1 m3 of concrete weighs 2190 kg.
- XY triangle
Determine area of triangle given by line -7x+7y+63=0 and coordinate axes x and y.
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
- Spherical segment
Spherical segment with height h=8 has a volume V=294. Calculate the radius of the sphere of which is cut this segment.
The shooter fired to a target from distance 9 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 16'(angle degree minutes). How many points should win his shot?
Average climb of the road is given by ratio 1:29. By what angle road average climb?
- Triangle angles
The angles α, β, γ in triangle ABC are in the ratio 10:5:6. Calculate size of angles.
- Black building
Jordan built building with a rectangular shape 5 m × 5.1 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenching
How far can you see from the ship's mast, whose peak is at 11 meters above sea level? (Earth's radius is 6370 km).
- Octahedron - sum
On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also.
Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
- Circle in rhombus
In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 18 cm and 17 cm. Calculate the circle area.
Determine the smallest integer which divided 8 gives remainder 6 when divided 19 gives remainder 9 and when divided by 11 gives remainder 2.
- Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
- Plasticine ball
Plasticine balls have radius r1=100 mm, r2=48 cm. For these balls are molded one big ball. Calculate the radius r of the resulting ball.
- Mystery of stereometrie
Two regular tetrahedrons have surfaces 48 cm2 and 108 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
A cyclist is moving at 26 km/h and follow pedestrian who is walking at speed 7 km/h. Walker has an advantage 13 km. How long take cyclist to catch up with him?
What must be the elevation of an observer in order that he may be able to see an object on the earth 814 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.