Examples for 9th grade - page 13
- 2x cone
Circular cone height 76 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
- Circle section
Equilateral triangle with side 34 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
- Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
Rhombus-shaped jewel have area of 153 mm2 and the edge in long 13.9 mm. Calculate the size of rhombus acute angle.
- 4s pyramid
Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
- Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
- Circle and angle
What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
- RT - hypotenuse and altitude
Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
- Football league
In the 5th football league is 10 teams. How many ways can be filled first, second and third place?
The count of accidents in 1995 caused 8780 women which is 8.4%. How many men caused the accidents?
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
Ping pong balls have a diameter of approximately 4.6 cm. They are sold in boxes of 4 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w
- The chord
Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
- Painter Pavel
Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.
Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?