Examples for 8th grade - page 25
- Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
- Two valves
Water fill the pool by two valves for 16 days. After 6 days the first valve was stopped and the second valve fill pool for 12 days. How many days took to fill the pool each of the valves individually?
- Ladislav in Amsterdam
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 2184. Calculate how many books Ladislav could buy at the price of 42 and 28 euros if he don't want fill whole home library and he can buy only 63 books?
- Hexagonal pyramid
Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high.
Which of the pairs of numbers on the number line encloses the longest segment: ?
- Fixed expenses 2013
Since 2013, the Slovak government plans to tax more small one person businesses. Instead of fixed expences 40% will be fixed expences 40% of gross income up to 420 Eur. Calculate what percentage of fixed expences will in 2013 pays from gross income 1093 E
- Prism - box
The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm3. Calculate the surface of the prism.
If the segment of the line y = -8x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone?
The elections attended a total 4436 voters. First day 32 men more than women, the second day 38 women more than men. How many women attended elections?
- Triangle SAA
The triangle has one side long 34 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.
- Equilateral cylinder
Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 221 cm3 . Calculate the surface area of the cylinder.
Fresh mushrooms contain 96% water, dried 12%. How many kg of fresh mushrooms is needed to collect to get 7 kg dried?
Determine the area of a trapezoid with bases 60 and 37 and height is 3 shorter than the its leg.
- Snowman 2
On the medal, which has the shape of a circle with a diameter 17 cm is sketched snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over snowman is the same as under it, 3. diameters of all circles express
- Rhombus diagonal
Area of rhombus is 417. One diagonal measures 45, find length of other diagonal.
- Vertical prism
The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
Calculate radius of the Circumscribed circle in the rectangle with sides 17 and 16. It can be rectangle inscribed by circle?
- Chord AB
What is the length of the chord AB if its distance from the center S of the circle k(S, 71 cm) is 27 cm?
Pedestrian came started at 7h in the morning with speed 3.6 km/h. At half-past eleven cyclist started at 27 km/h same way. How many minutes take cyclist to catch up pedestrian?