Examples for 9th grade - page 9
- Pyramid roof
1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
- Cylinder - basics
Cylinder with base radius r = 37 cm and height h=74 cm. Calculate:
- ISO triangle
Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 128 mm.
At 15:20 the ship set sail at 16 km/h. At 17:50 followed by at 41 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took?
Cylinder shell has the same content as one of its base. Cylinder height is 25 m. What is the radius of the base of the cylinder?
- Climb in percentage
The height difference between points A and B is 442 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 6.8 km.
- Rotary cone
The volume of the rotation of the cone is 104 cm3 and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone.
- Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 7 cm.
- Hollow sphere
Calculate the weight of a hollow brass sphere (density 8.5 g/cm3), if the outer diameter is 10 cm and wall thickness is 3 mm.
- Profitable bank deposit 2012
Calculate the value of what money lose creditor with a deposit € 7700 for 4 years if the entire duration are interest 2.2% p.a. and tax on interest is 19% and annual inflation is 3.6% (Calculate what you will lose if you leave money lying idle at negative
How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 13 m and the angle at the vertex of the axial section is 150°?
- Diagonals of the rhombus
Calculate height of rhombus whose diagonals are 15 cm and 5 cm.
- Gold wire
From one gram of gold was pulled wire 1.2 km length. What is it diameter if density of Au is ρ=19.5 g/cm3?
From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 39 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?
- Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=7 m.
- Equilateral triangle
How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 7 mm from it?
- Triangular prism
Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 50 degrees, |AB| = 5 cm. Calculate the volume of the prism.
Between cities A and B is route 3 km long of rise average 4‰. Calculate the height difference of cities A and B.
Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
- Right isosceles
Calculate area of the isosceles right triangle which perimeter is 35 cm.