Pythagorean theorem + power - practice problems - last page
Number of problems found: 79
- Quadrilateral PQRS
PQRS is a quadrilateral with P(4,4), S(8,8), and R(12,8). If vector PQ=4*vector SR, find the coordinates of Q. Solve it - Center
Calculate the coordinates of the circle center: x² -4x + y² +10y +25 = 0 - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
- Quadrilateral 29201
How much sheet is needed for a roof with the shape of a regular quadrilateral pyramid if its edge is 2.8 m long and the height of the roof is 0.8 m?Calculate 10% for the overlap (extra). - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Sandpile
Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the base's circumference and the length of both sides of the cone (over the top). What is the sand cone's volume if t - Tank
In the middle of a cylindrical tank with a bottom diameter of 251 cm is a standing rod that is 13 cm above the water surface. If we bank the rod, its end reaches the water's surface just by the tank wall. How deep is the tank? - Triangular prism
The triangular prism has a base in the shape of a right triangle, the legs of which are 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²?
- Quadrilateral 21523
Calculate the surface area and volume of a regular quadrilateral pyramid if the edge of the lower base is 18 cm and the edge of the upper base is 15 cm. The wall height is 9 cm. - Calculate 4842
The area of the rotating cylinder shell is half the area of its surface. Calculate the surface of the cylinder if you know that the diagonal of the axial section is 5 cm. - Surface area of the top
A cylinder is three times as high as it is wide. The length of the cylinder diagonal is 20 cm. Find the exact surface area of the top of the cylinder. - Cuboid
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges. - Floating barrel
The barrel (cylinder shape) floats on water, the top of the barrel is 8 dm above water, and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
- Body diagonal
The cuboid has a volume of 32 cm³. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Diagonals 5551
The cube has a wall area of 81 cm². Calculate the length of its edge, wall, and solid diagonals. - Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonally. - Cube diagonals
Calculate the length of the side and the diagonals of the cube with a volume of 27 cm³. - Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long?
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