Volume + quadratic equation - math problems
Number of problems found: 37
- The surface
The surface of the cylinder is 1570 cm2, its height is 15 cm. Find its volume and radius of the base.
- Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm2 greater than the upper base's content. Calculate the area of the upper base.
- 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.
Consider all square prisms with a height of 10 cm. If x is the measurement of the base edge, in cm, and y is the volume of the prism, in cm3. Graph the function
- 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.
- Rotary cylinder
In the rotary cylinder it is given: surface S = 96 cm2 and volume V = 192 cm cubic. Calculate its radius and height.
- Hard cone problem
The surface of the cone is 200 cm², its height is 7 centimeters. Calculate the volume of this cone.
- Consecutive members
The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, 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.
- The pool
The cube-shaped pool has 140 cubic meters of water. Determine the dimensions of the bottom if the depth of the water is 200 cm and one dimension of the base is 3 m greater than the other. What are the dimensions of the pool bottom?
- Shell area cy
The cylinder has a shell content 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.
- 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.
- Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, √13cm. Calculate the surface and volume of the block.
- Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
- Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 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.
- Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), then find the cuboid volume. Solve for x=1.3, y=1, z=1.2
- Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours longer and the second pipe 9 hours longer than both pipes open at the same time?
- Cuboid walls
If the areas of three adjacent faces of a cuboid are 8 cm², 18 cm² and 25 cm². Find the volume of the cuboid.
- 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.
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