Examples for 9th grade - page 59
- Brass tube
The outer perimeter of brass tube (ρ = 8.5 g/cm3) is 51 cm. Its mass is 5 kg, length 56 cm. What is the pipe wall thickness?
- Silver medal
To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus.
- Water well
Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?
- Blackjack TU160
Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. At
- Trapezoid RT
The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio
- Giant coin
From coinage metal was produced giant coin and was applied so much metal, such as production of 10 million actual coins. What has this giant coin diameter and thickness, if the ratio of diameter to thickness is the same as a real coin, which has a diameter
- Trapezoid v3
The isosceles trapezoid has the angle at a firsst base 40 degrees less than the angle at second base. How large angles has this trapezoid ?
- Chemical parison
The blown parison (with shape of a sphere) have a volume 1.3 liters. What is its surface?
- High wall
I have a wall 2m high. I need a 15 degree angle (upward) to second wall 4 meters away. How high must the second wall?
- Tin with oil
Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
- Juice box 2
Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of the
On double-track express met with a freight train. Express travel at speed 72 km/h, a freight train at speed 36 km/h. After what time period will be from 9 km apart?
- Garden pool
Mr. Novak fill garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool?
- Angles of the triangle
ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
- Repair company
The company repairs cars. The first day repair half of the contract second day, the half of the rest and third day 6 residue cars. How many total cars company repaired?
- Concentric circles
In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord.
- Three men
Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
- RT and ratio
Right triangle whose cathetus are in a ratio 6:17 has hypotenuse 47 m long. How long are cathetus?
- Water reservoir
The cuboid reservoir contains 2200 hectoliters of water and the water height is 2.9 m. Determine the dimensions of the bottom where one dimension is 2.1 m longer than the second one.