Geometry - math word problems - page 145 of 162

Number of problems found: 3238

Largest possible cone
It is necessary to make the largest possible cone from an iron rod in the shape of a prism with dimensions of 5.6 cm, 4.8 cm, and 7.2 cm. a) Calculate its volume. b) Calculate the waste.
Calculate 19543
Calculate the surface of a prism with a square base whose mantle is a rectangle with sides of 18cm and 8cm. How many solutions does the task have? List all solutions.
Center of gravity
The mass points are distributed in space as specified by coordinates and weight. Find the center of gravity of the mass points system: A₁ [-17; 10; 9] m₁ = 23 kg A₂ [-16; -19; 0] m₂ = 31 kg A₃ [4; -14
Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000m, and its crew needs the ship to carry the collected research material in a cuboid box with a square base. Determine the length of the base and (and height h) so that the box has the large
Cube zoom
If we magnify the cube's edge by 47 %, how many percent does this increase the cube's volume and surface?
Identical 35961
Nine identical spheres are stacked in the cube to fill the cube's volume as much as possible. What part of the volume will the cube fill?
Calculate 81935
The volume of the cuboid is 960 cm³. The lengths of the edges are in the ratio 1 : 3: 5. Calculate the surface area of the cuboid.
Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
Cuboid - edges
The cuboid has dimensions in a ratio of 4:3:5. The shortest edge is 12 cm long. Find: The lengths of the remaining edges The surface of the cuboid The volume of the cuboid
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?
Kilograms 66864
The sculptor composes an ice city from ice cubes. The cube with an edge length of 2 dm weighs 7.2 kg. How many kilograms is an ice cube with an edge length of 6 dm heavier than it?
Brass tube
The outer perimeter of the brass tube (ρ = 8.5 g/cm³) is 38 cm. Its mass is 5 kg, length 54 cm. What is the pipe wall thickness?
Determined 3570
There are 12 points in space, with no three lying on a straight line. How many different planes are determined by these points?
Downstream 7002
A rowboat sailing down a river covers a distance of 120 m downstream in 12 s and upstream in 24 s. Find the magnitude of the ship's velocity relative to the water and the current in the river. Both speeds are constant.
Construct 61253
Using Euclid's theorem, construct a line of length √15.
Weight of air
What is the weight of air in the living room measuring width 6 m, length 4 m, and height 2.56 m? Air density is ρ = 1.2959 kg/m³.
Lampshade
The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm² of material will we need when 10% is waste?
Rectangular cuboid
The rectangular cuboid has a surface area 4131 cm², and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
Calculate 81936
The volume of the block is 7,500 dm³. The lengths of the edges are in the ratio 3: 4: 5. Calculate the surface area of the cuboid.
Equilateral 81142
The rotating body was created by rotating an equilateral triangle with a side length of a=2 cm around one of its sides. Calculate the volume of this rotating body.

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