Basic operations and concepts - math word problems - page 313 of 332
Number of problems found: 6633
- Ratio 52
The ratio of the surface area of a cube to its volume is 2:1. Calculate: a) the edge length of the cube in cm, b) the volume of the cube in cm³, c) the surface area of the cube in cm². - Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm. - The coil
How many ropes (a diameter of 8 mm) fit on the coil (threads are wrapped close together)? The coil has the following dimensions: The inner diameter is 400 mm. The outside diameter is 800 mm. The length of the coil is 470 mm. - Cone cutout
The cone shell with a base radius of 20 cm and a height of 50 cm unfolds into a circular cutout. How big is the center angle of this cutout? - Alien ship
The alien ship has the shape of a sphere with a radius of r = 3000 m, 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 larg - 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? - Area and percents
Find what percentage is a smaller cube surface when the wall's surface area decreases by 25%. - Drug effectiveness probability
According to clinical studies, the effectiveness of the drug is 90%. The doctor prescribed the medicine to eight patients. What is the probability that the drug will be effective in all these patients? - Points in plane
The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points? - Pentagon
The signboard has the shape of a pentagon ABCDE, in which line BC is perpendicular to line AB, and EA is perpendicular to line AB. Point P is the heel of the vertical starting from point D on line AB. | AP | = | PB |, | BC | = | EA | = 6 dm, | PD | = 8.4 - Suppose 4
Suppose that 14% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped). Consider a random sample of 200 shafts, and let X denote the number among these that are nonconforming and can be - 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. - Cuboid Edges from Surface
The edges of a cuboid are in the ratio 1:2:3. Calculate their length if you know that the surface of the entire cuboid is S=5632 m². Then, perform a test to ensure the calculation is correct. - Triangle cone rotation
A thin plate in the shape of a right-angled triangle is turned once around the shorter hanger and a second time around the longer hanger. Cones are described by rotation. Are they the same volume? The dimensions are: shorter pendant 6 cm, longer pendant 8 - Prism surface calculation
Calculate the surface of a prism with a square base whose mantle is a rectangle with sides of 18 cm and 8 cm. How many solutions does the task have? List all solutions. - Block edge dimensions
How many blocks have integer dimensions of the edges if the surface is 48 m²? - Distance - cities
Determine the actual distance between two cities if their distance on the map is 7.5 cm and the map scale is 1:60,000. - Plane count
There are 12 points in space, with no three lying on a straight line. How many different planes are determined by these points? - Cube edges length
If we reduce the length of the cube edge by 30%, this reduced cube has an area of 1176 cm². Specify the edge length and volume of the original cube. - Two bodies
The rectangle with dimensions 8 cm and 4 cm is rotated 360º first around the longer side to form the first body. Then, we similarly rotate the rectangle around the shorter side b to form a second body. Find the ratio of surfaces of the first and second bo
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