# Examples for 8th grade - page 69

- Garden pond

Concrete garden pond has bottom shape of a semicircle with a diameter 1.1 m and is 47 cm deep. Daddy wants make it surface. How many liters of water is in pond if watel level is 22 cm? - Mystery of stereometrie

Two regular tetrahedrons have surfaces 48 cm^{2}and 108 cm^{2.}In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Park

In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m. - Total displacement

Calculate total displacement of the 12-cylinder engine with the diameter of the piston bore B = 6.8 cm and stroke S=2 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back t - Slope form

Find the equation of a line given the point X(10, -2) and slope -1.2. Arrange your answer in the form y = ax + b, where a, b are the constants. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 7:10:8 and if you know that the wall diagonal AC is 21 cm and angle between AC and the body diagonal AG is 40 degrees. - Cups

We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then - Cone

Calculate volume and surface area of the cone with diameter of the base d = 12 cm and side of cone with the base has angle 41°47'59″. - Cone

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? - Cylinders

Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much? - Trains for people

It is said that the train is synonymous to delay. Calculate the average speed of travel by train long 50 km, with regular train leave at 6:05 and arrive at 7:20, but train is late and has departure at 9:52 and arrive at 11:05. - Square 2

Points D[9,-1] and B[3,3] are opposed vertices of the square ABCD. Calculate area of the square ABCD. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm^{2.} - Chord MN

Chord MN of circle has distance from the center circle S 118 cm. Angle MSN is 41°. Determine the radius of the circle. - Carbon dioxide

Calculate how many grams of oxygen are in 126 g of carbon dioxide CO_{2}. Relative atomic mass of oxygen is 16 and of carbon is 12. - Extreme temperatures

USA hit extreme heat wave. Calculate percentage of the air temperature change from normal summer temperature 24 °C to 37 °C. - Widescreen monitor

Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 17 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha - Discounts on rail (ZSSK)

The railway company ZSSK offers a discount of 40% (JUNIOR RAILPLUS EURO - Cone in cube

The cube is inscribed cone. Determine the ratio of the volume of cone and cube. The ratio express as a decimal number and as percentage. - 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.

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