Basic operations and concepts - math word problems - page 302 of 323
Number of problems found: 6445
- Pyramid cut
We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has an area of 10 cm². Find the area of the or - Aquarium Dimensions and Volume
The aquarium dimensions are in the ratio a: b: c = 5:2:4. 6600 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? - Rectangle dimensions
The rectangle has a circumference of 24 cm so that its area is maximum and its length is larger than its width. Find the dimensions of a rectangle. - The cone
The cone has a base radius of 12 cm and a height of 20 cm. It was truncated at 6 cm from the base. We created a truncated cone - frustum. Find the radius of the base of the truncated cone. - The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm, and height v = 5 cm. What is the volume of the cone from which the truncated cone originated? - Volume of sphere
How many times does the volume of a sphere increase if its radius increases two times? - Cube Edge Volume Change
How does the volume of a cube change if we double the length of its edge? - Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase? - Tetrahedron water level
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise? - Right circular cone
The volume of a right circular cone is 5 liters. The cone is divided by a plane parallel to the base, one-third down from the vertex to the base. Calculate the volume of these two parts of the cone. - Block material calculation
How many square meters of material is needed to make two identical blocks with dimensions of 6 dm, 8 dm, and 12 dm if we count 8% of the material for folds? (Round to two decimal places. ) - Z score transformation
The annual salary of an entry-level statistics major (in thousands of dollars) is normally distributed with a mean of 75 and a standard deviation of 12. X ∼ N ( μ = 75, σ = 12 ). What minimum salary should a statistics major aim for to earn amongst the to - Pyramid roof
How much m² of the galvanized sheet is used to cover the roof of the tower, which has the shape of a four-sided pyramid, whose base edge is 6 m long? The height of the tower is 9m. When covering, is 5% metal waste expected? - Grade point average
The average GPA is 2.78, with a standard deviation of 0.45. If GPA is normally distributed, what percentage of the students have the following GPAs? Solve for the z-score and report the appropriate percentage: a. Less than 2.30 b. Less than 2.00 c. More t - Largest wall
Find the area of the largest wall of a prism with a rectangle base with a height of 4 dm, side c = 5 cm, and side b = 6 cm. - Earth's surface
The greater part of the Earth's surface (r = 6371 km) is covered by oceans; their area is approximately 71% of the Earth's surface. What is the approximate area of the land? - Cylindrical tank
The cylinder-shaped tank with a diameter of 100 cm is 50% full and contains 7850 l of water. What is the height of the tank? - Cone Radius Sector Angle
Determine the cone's base's radius if its shell develops into a circular section with radius "s" = 10 and center angle x = 60 °. r = ?, o =? - Ratio of edges
The cuboid dimensions are in a ratio of 3:1:2. The body diagonal has a length of 28 cm. Find the volume of a cuboid. - Prism volume calculation
The prism with a diamond base has one base diagonal of 20 cm and a base edge of 26 cm. The edge of the base is 2:3 to the height of the prism. Calculate the volume of the prism.
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