Examples for 8th grade - page 45
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg?
- Circular flowerbed
Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle.
- Dig water well
Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out?
- Rectangular trapezoid
Calculate the content of a rectangular trapezoid with a right angle at the point A and if |AC| = 4 cm, |BC| = 3 cm and the diagonal AC is perpendicular to the side BC.
- Midpoint of segment
Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B?
- Oil tank and pipes
The underground oil tank can be filled by two oil pipelines. The first is filled in 72 hours and the second in 48 hours. How many hours from the moment when first pipeline began to fill the oil is it necessary to start filling it with the second to fill in
How many times turns the wheel of a passenger car in one second if car run at speed 100 km/h. Wheel diameter is d = 62 cm.
In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.
- The carpet
How many meters of carpet 90 cm wide need to cover floor room which has a rectangular shape with a lengths 4.8 m and 2.4 m if the number of pieces on the carpet is needed to be lowest?
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
- Barrel 2
Empty barrel weighs 7 kg. When it filled with water up to 45% height, weighs 60 kg. How heavy is barrel full of water?
Both dimensions of the rectangular parcel were increased by 26%. By how many % has increased its acreage?
- Total displacement
Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 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.
- Round table tablecloth
Round table has area 50.24 dm2. Calculate the diameter of the circular tablecloth, if it is extend beyond the edge of the table by 30 cm.
Small tractor wheel with a diameter of 60 cm must be rotated 8 times to overcome some pathway. How many times must turn the big tractor wheel with a radius 60 cm to overcome the same distance?
- RT 10
Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
Outer perimeter of silo is 32 m. Concrete wall is 35 cm thick. What is diameter and area of inside floor of silo?
- Chicken and rabbits (classic)
Grandmother breeding chickens and rabbits. It found that the yard has 35 heads and 108 legs. How many chickens and rabbits breeding in the yard?
- Miraculous tree
Miraculous tree grows so fast that the first day increases its height by half the total height of the second day by the third, the third day by a quarter, etc. How many times will increase its height after 6 days?