Examples for 9th grade - page 65
Funicular on Petrin (Prague) was 408 meters long and overcomes the difference 106 meters in altitude. Calculate the angle of climb.
A diagonal of a rhombus is 20 cm long. If it's one side is 26 cm find the length of the other diagonal.
- Prism bases
Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
- Equation with abs
Solve this equation with absolute value member: ?
- Hexagon rotation
A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
- Elimination method
Solve system of linear equations by elimination method: 5/2x + 3/5y= 4/15 1/2x + 2/5y= 2/15
James and Jaroslav are friends. Together they had 48 toy cars. But if John took 8 cars from Jaroslav, Jaroslav will be have 1.5 times more toy cars than James. How many toy cars had Jaroslav and James?
- Unknown number 7
Calculate unknown number whose 12th power when divided by the 9th power get a number 27 times greater than the unknown number. Determine the unknown number.
- Right triangle
It is given a right triangle angle alpha of 90 degrees beta angle of 55 degrees c = 10 cm use Pythagorean theorem to calculate sides a and b
- Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
Solve quadratic equation: ?
- Surface area of cylinder
Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.
- Circle's chords
In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
- Four friends
Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together?
- Horizontal Cylindrical Segment
How much fuel is in the tank of horizontal cylindrical segment with a length 10m, width of level 1 meter and level is 0.2 meters below the upper side of the tank?
- Tetrahedral pyramid
It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
- Pyramid in cube
In a cube with edge 12 dm long we have inscribed pyramid with the apex at the center of the upper wall of the cube. Calculate the volume and surface area of the pyramid.
- Sphere vs cube
How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
- Sphere vs cube
How many percent of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?