Solid geometry + quadratic equation - practice problems
Number of problems found: 67
- Dimensions 6130
The aquarium dimensions are in the ratio a: b: c = 5:2:4. 6609 cm² of glass was used for its production. How many liters of water will fit in the aquarium if it reaches 5 cm below its edge? - Cuboid walls
Calculate the cuboid volume if its different walls have an area of 195cm², 135cm², and 117cm². - The cylinder
In a rotating cylinder, it is given: the surface of the shell (without bases) S = 96 cm² and the volume V = 192 cm cubic. Calculate the radius and height of this cylinder. - Two cubes
The surfaces of two cubes, one of which has an edge of 22 cm longer than the second, differ by 19272 cm². Calculate the edge length of both cubes. - Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm² and volume V = 192 cm cubic. Calculate its radius and height. - Cubes
Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm². Determine the length of the edges of these cubes. - Determine 73454
The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm. - The block
The block, the edges formed by three consecutive GP members, has a surface area of 112 cm². The sum of the edges that pass through one vertex is 14 cm. Calculate the volume of this block. - Calculate 62864
The block volume is 1440 cm3, its surface is 792 cm2, and the area of one of its walls is 92 cm². Calculate the lengths of its sides. - Consecutive members
The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, and c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence. - Swimming pool
The pool shape of a cuboid is 299 m³, full of water. Determine the dimensions of its bottom if the water depth is 282 cm and one bottom dimension is 4.7 m greater than the second. - Shell area cy
The cylinder has a shell area of 300 cm square, while the height of the cylinder is 12 cm. Calculate the volume of this cylinder. - The cylinder
The cylinder has a surface area of 300 square meters, while the cylinder's height is 12 m. Calculate the volume of this cylinder. - 3rd dimension
The block has a surface of 42 dm2, and its dimensions are 3 dm and 2 dm. What is the third dimension? - Water reservoir
The cuboid reservoir contains 1900 hectoliters of water, and the water height is 2.5 m. Determine the bottom dimensions where one dimension is 3.2 m longer than the second. - Hard cone problem
The cone's surface is 200 cm², and its height is 7 centimeters. Calculate the volume of this cone. - Cylinder diameter
The surface of the cylinder is 149 cm². The cylinder height is 6 cm. What is the diameter of this cylinder? - Assembling 63964
Little Pavel was assembling building blocks (a cube is shaped like a cube). He wanted to build a big cube. However, he had 75 dice left, so he increased the edge by one die. Then he was missing 16 dice. How many cubes did he have in the kit? - Magnified cube
If the lengths of the cube's edges are extended by 5 cm, its volume will increase by 485 cm³. Determine the surface of both the original and the magnified cube. - The surface
The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10cm.
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