Examples for 9th grade - page 10
- Triangular prism
Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 50 degrees, |AB| = 5 cm. Calculate the volume of the prism.
In the center of the cube with edge 15 cm we will drill cylinder shape hole. Volume of the hole must be 28% of the cube. What drill diameter should be chosen?
- Cu wire
Copper wire has a length l = 210 m and diameter d = 10 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
- Similarity coefficient
The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle.
Product has been discounted twice by 14%. What is the total discount given?
Three metal balls with volumes V1=41 cm3 V2=58 cm3 and V3=83 cm3 melted into one ball. Determine it's surface area.
- Axial section
Axial section of the cylinder has a diagonal 15 cm long and we know that the area of the side and the area of base is in ratio 1:1. Calculate the height and radius of the cylinder base.
From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 39 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?
How many ways are there to arrange 9 books on a shelf?
Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60°
- Diofant 2
Is equation ? solvable on the set of integers Z?
How long path will walk the end of the clock's minute-hand long 24 cm for 110 minutes? How long will walk in the same time hour-hand?
How high is the building that throws horizontal shadow 58.5 m long at angle 36°36'?
- Square diagonal
Calculate the length of diagonal of the square with side a = 18 cm.
Cube, which consists of 27 small cubes with edge 3 dm has volume:
- Triangle ABC
Right triangle ABC with right angle at the C, |BC|=20, |AB|=35. Calculate the height of the triangle hAB to the side AB.
During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 5 hours. How many hours will spend washing the windows this "women's team" if working togethe
On the tourist map at a scale of 1 : 100000 is distance between two points along a straight road 5.4 cm. How long travels this distance on a bike at 23 km/h? Time express in minutes.
- Diofant equation
In the set of integers (Z) solve the equation: ? Write result with integer parameter ? (parameter t = ...-2,-1,0,1,2,3... if equation has infinitely many solutions)
In the city are 2/6 of women married for 4/4 men. What proportion of the townspeople is free (not married)? Express as a decimal number.