Tangent - practice for 14 year olds - page 8 of 9
Number of problems found: 180
- Road drop
On a straight stretch of road is marked a 12 percent drop. What angle makes the direction of the road with the horizontal plane? - Pyramid 8
Calculate the volume and the surface area of a regular quadrangular pyramid with a base side of 9 cm and a side wall with the base has an angle of 75°. - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - Height difference
What height difference is overcome if we pass a road 1 km long with a pitch21 per mille?
- Chimney
The lower circumference of the chimney is 12.57 m, and the top circumference is 5.655 m. The slope of the walls is 87°. Find the height of the chimney. - Flowerbed
Flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be plante - Bevel
I have a bevel in the ratio 1:6. What is the angle, and how do I calculate it? - Building elevation angle
In the building, I focused at an angle 30°. When I moved the 5 m building, I focused at an angle 45°. What is the height of the building? - Tree
How tall is the tree observed in the visual angle of 52°? If I stand 5 m from the tree and my eyes are two meters above the ground.
- Angle
A straight line p given by the equation y = (-8)/(6) x +78. Calculate the size of the angle in degrees between line p and y-axis. - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c has dimensions in the ratio of 7:8:10. If you know that the diagonal wall AC is 56 cm, and the angle between AC and space diagonal AG is 25 degrees. - Slope of the pool
Calculate the slope (rise:run) of the bottom of the swimming pool long 10 m. The water depth at the beginning of the pool is 0.96 m (for children), and the depth at the end is 1.86 m (for swimmers). Slope express as a percentage and as the angle in degree - Map - climb
On the map of the High Tatras, on a scale of 1:11000, are cable car stations in the Tatranska Lomnica and the Skalnate Pleso with a distance of 354.6 mm. The altitude of these stations is 949 m and 1760 m. What is the average angle of climb on this cable
- Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Isosceles trapezoid
Isosceles trapezoid ABCD, AB||CD is given by |CD| = c = 12 cm, height v = 16 cm and |CAB| = 20°. Calculate area of the trapezoid. - Pyramid
Pyramid has a base a = 3cm and height in v = 15 cm. a) calculate the angle between plane ABV and the base plane b) calculate the angle between opposite side edges. - Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Diagonals
The rhombus has two diagonals, e=14 dm, and f=11 dm. Calculate the side angle and height of the rhombus.
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