# 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. - Hole

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/m^{3.}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. - Discount

Product has been discounted twice by 14%. What is the total discount given? - Balls

Three metal balls with volumes V_{1}=41 cm^{3}V_{2}=58 cm^{3}and V_{3}=83 cm^{3}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. - Tourists

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? - Shelf

How many ways are there to arrange 9 books on a shelf? - Cuboid

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? - Clocks

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? - Building

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. - Cubes

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 h_{AB}to the side AB. - Madams

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 - Map

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) - Freedom

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.

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