# Examples for 8th grade - page 26

- Semicircle

In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Tank and water

Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in? - Rail turn

The curve radius on the railway line is 532 m . Length of rail track on it is 818 m. How many degrees is the angle ASB, if A and B are boundary points and S is center of arc curve. - Cone

If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Hairs

Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it is - Two valves

Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 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 € 3484. Calculate how many books Ladislav could buy at the price of 48 and 52 euros if he don't want fill whole home library and he can buy only 70 books? - 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 1569 E - Sun rays

If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei - Series

Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ? - Tributaries

The first tributary fill pool with water in 15 hours. The second tributary fill pool in 10 hours. For how many hours the pool is filled with both tributaries? - 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 - Segments

Which of the pairs of numbers on the number line encloses the longest segment: ? - Mushrooms

Fresh mushrooms contain 94% water, dried 14%. How many kg of fresh mushrooms is needed to collect to get 10 kg dried? - Common chord

Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles? - Rhombus diagonal

Area of rhombus is 224. One diagonal measures 33, find length of other diagonal. - Basements

In the first basement is more flies than the spiders, the second vice versa. Each basement had spiders and flies together 100 feet. Determine how many could be flies and spiders in the first and second basement. PS. We only need, when you write how many. - Leg

Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg. - Loan

Apply for a $ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity. - Triangle SAA

The triangle has one side long 71 m and its two internal angles is 60°. Calculate the perimeter and area of the triangle.

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