Body volume + expression of a variable from the formula - math problems
Number of problems found: 211
- Triangular prism
The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
- Quadrilateral pyramid,
A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
- Water tank
What is the height of the cuboid-shaped tank with the bottom dimensions of 80 cm and 50 cm if the 480 liters of water reaches 10 cm below the top?
How deep is the pool if there are 2025 hectoliters of water and the bottom dimensions are a = 15 meters b = 7,5 meters and the water level is up to 9/10 (nine-tenths) of height.
- 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.
The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil.
- Two rectangular boxes
Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
- Octagonal prism vase
0.7 l of water can be poured in an octagonal prism vase. What is the height of the vase, if the bottom has a area of 25 cm square and a thickness of 12 mm?
- Surface of cubes
Peter molded a cuboid 2 cm, 4cm, 9cm of plasticine. Then the plasticine split into two parts in a ratio 1:8. From each piece made a cube. In what ratio are the surfaces of these cubes?
- 3d printer
3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)
- Water in aquarium
The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water.
- Third dimension
Calculate the third dimension of the cuboid: a) V = 224 m3, a = 7 m, b = 4 m b) V = 216 dm3, a = 9 dm, c = 4 dm
Calculate how many liters of air will fit in the tent that has a shield in the shape of an isosceles right triangle with legs r = 3 m long the height = 1.5 m and a side length d = 5 m.
- 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. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure.
- Horizontal Cylindrical Segment
How much fuel is in the horizontal cylindrical segment tank with a length of 10m, the width of level 1 meter, and the level is 0.2 meters below the tank's upper side?
- Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, and its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
- Frustum of a cone
A reservoir contains 28.54 m3 of water when full. The diameter of the upper base is 3.5 m, while at the lower base is 2.5 m. Find the height if the reservoir is in the form of a frustum of a right circular cone.
- Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m3 of soil were excavated when digging the pit?
- Fuel economy
How many kilometers is sufficient petrol in the cylinder fuel tank with a diameter 40 cm and the base of tank length 1 m, when it is filled to 60% and if the car consume 15 liters per 100 km?
- The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm