Volume + third power - practice problems - page 5 of 6
Number of problems found: 115
- Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge if you know that the prism volume is 2187 cm³. - Cube zoom
How many percents do we increase the volume and surface of the cube if we magnify its edge by 47 %? - Cuboid and ratio
A cuboid has a volume of 810 cm³. The lengths of edges from the same vertex are in a ratio of 2:3:5. Find the dimensions of a cuboid. - 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 - Measuring 6188
Find the length of the cube's edge and its volume is equal to 60% of the volume of a block measuring 7 cm, 8 cm, and 6 cm. - Decreases 5625
How much percent will the surface and volume of the cube decrease if the diagonal decreases by 10%? b) if the diagonal increases by 10%? - Two pots
Two similar pots have 16 cm and 10 cm heights if the smaller pot holds 0,75 l. Find the capacity of the larger pot - Sphere volume formula
If V=4/3 π r³, find the value of V when r = 7, the value of r when V=113 1/7 - 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. - Cube-shaped box
Find the size of the smallest possible cube-shaped box where three types of 3cm, 5cm, 6cm small cubes could be stacked to fully use the box space (each type of cube separately). Can you find out how many smallest cubes are in the box? - Equilateral cylinder
The equilateral cylinder (height = base diameter; h = 2r) has a V = 272 cm³ volume. Calculate the surface area of the cylinder. - Surface 45911
A large cube with an edge of length 3 is given. One small cube with a volume 27 times smaller than the volume of the large cube is glued to each of its faces. All the small cubes touch the big ones through the wall. What surface does this body have? - Completely 4226
The aquarium is shaped like a cube and is partially filled with water. For Peter, a cube with an edge of 8 cm fell into it and completely sank. The water level in the aquarium rose by 1 cm. What is the volume of the whole aquarium? - An architect 2
An architect is designing a house. He wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume - Balls
Three metal balls with volumes V1=81 cm³ V2=96 cm³ and V3=28 cm³ melted into one ball. Determine its surface area. - Seawater
Seawater density is 1025 kg/m³, and ice is 920 kg/m³. Eight liters of seawater froze and created a cube. Calculate the size of the cube edge. - Prism bases
Volume perpendicular quadrilateral prism is 360 cm³. The edges of the base and height of the prism are in the ratio 5:4:2. Find the area of the base and walls of the prism. - Two boxes-cubes
Two boxes of a cube with edges a=28 cm and b = 92 cm are to be replaced by one cube-shaped box (same overall volume). How long will its edge be? - Wall thickness
The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm³. - For thinkings
The glass cube dives into the aquarium, which has a length of 25 cm, a width of 20 cm, and a height of 30 cm. Aquarium water rises by 2 cm. a) What is the volume of a cube? b) How many centimeters measure its edge?
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