Pythagorean theorem + quadratic equation - practice problems - last page
Number of problems found: 118
- Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find the value of x - MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the ball's surface was 8 cm. Find the diameter of John's ball. - 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. - 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.
- Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and the body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - 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? - Sphere from tree points
Equation of sphere with three point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - ABCDA'B'C'D 6261
The ABCDA'B'C'D 'prism has a square base. The wall diagonal of the AC base is 9.9 cm long, and the body diagonal AC 'is 11.4 cm long. Calculate the surface area and volume of the prism.
- 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. - 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? - Stadium
A domed stadium is shaped like a spherical segment with a base radius of 150 m. The dome must contain a volume of 3500000 m³. Determine the dome's height at its center to the nearest tenth of a meter.
- Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block.
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