Task 1 · easy
Location of straight cube
In the ABCD cube A′B′C′D′ consider simple AB and CC′. Are they intersecting, are they parallel or diagonal? How are their directions set?
Hint and solution →Original practice tasks · Math · High school . Class 3
Stereometry — tasks with solutions
Start with the easier exercises and work your way up. Every task has a hint and a full step-by-step solution — try it on your own first, then unlock the solution and compare.
Easy
7
Medium
6
Hard
7
Task 2 · easy
Diagonal of the rectangle
The rectangle is dimensions 3, 4 and 12. Calculate the diagonal of the solids.
Hint and solution →Task 3 · medium
Straight angle
The normal square root has a base side 4 and a height of 41⁄2. Calculate the angle between the diagonal of the solid and the plane of the base.
Hint and solution →Task 4 · easy
Volume of the ridge
The base field of the ridge is 12 and the height is 10. Calculate volume.
Hint and solution →Task 5 · medium
Total Playback Field
The rectangle has a base of 3×4 and height 5. Calculate the total field.
Hint and solution →Task 6 · easy
Volume of pyramid
The spine has a square base with a side of 6 and a height of 4. Calculate volume.
Hint and solution →Task 7 · hard
Field of correct pyramid
The correct quadrilateral pyramid has a side of base 6 and a height 4. Calculate the total field.
Hint and solution →Task 8 · hard
Side edge angle with base
The correct quadrilateral pyramid has a base side of 6 and a height of 31⁄2. Calculate the angle between the side edge and the base plane.
Hint and solution →Task 9 · easy
Two-walled angle in the cube
What is the two-walled angle between the two adjacent walls of the cube?
Hint and solution →Task 10 · easy
Roller volume
The roller has a radius of 3 and a height of 5. Calculate volume.
Hint and solution →Task 11 · medium
Roller Total Field
The roller has a radius of 2 and a height of 7. Calculate the total field.
Hint and solution →Task 12 · hard
Angle in the axial section of the cylinder
The axial cross section of the cylinder is a rectangle of 6×8. The diagonal of this rectangle forms with the plane of the base of the angle α. Mark sinα and cosα.
Hint and solution →Task 13 · medium
Cone 3
The straight cone has radius 3 and height 4. Calculate the formation, volume and total field.
Hint and solution →Task 14 · hard
Forming angle with base
The straight cone has radius 3 and height 3⁄3. Calculate the β angle between the formation and the base plane.
Hint and solution →Task 15 · hard
Cone dilating angle
The straight cone is r=h. Calculate the full dilating angle of the cone in the axial section.
Hint and solution →Task 16 · easy
A bullet with a radius of 3
The bullet has a radius of 3. Calculate the area and volume.
Hint and solution →Task 17 · medium
Volume of a similar solid
The length scale of the larger block to the smaller one is 2. The volume is less than 15. Calculate the volume of the larger.
Hint and solution →Task 18 · medium
Volume scale
The volume of a larger solid similar to that of a larger body is 27 times that of a smaller volume. What's the length scale?
Hint and solution →Task 19 · hard
Radiation and roll field from volume
The cylinder has a volume of 100π and a height of 4. Calculate the radius and the total field.
Hint and solution →Task 20 · hard
Bridge extended cube cross section
Expansion range: cube has edge 4. The diagonal section has sides 4 and a diagonal wall 41⁄2. Calculate his field.
Hint and solution →Karta pracy do druku
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Otwórz kartę pracy →After the tasks
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