Volume + body volume - math problems

1. Right circular cone The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
2. Right pyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
3. Base of prism The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm2.
4. Pebble The aquarium with internal dimensions of the bottom 40 cm × 35 cm and a height of 30 cm is filled with two-thirds of water. Calculate how many millimeters the water level in the aquarium rises by dipping a pebble-shaped sphere with a diameter of 18 cm.
5. Steel tube The steel tube has an inner diameter of 4 cm and an outer diameter of 4.8 cm. The density of the steel is 7800 kg/m3. Calculate its length if it weighs 15 kg.
6. TV transmitter The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
7. Cube in a sphere The cube is inscribed in a sphere with volume 3234 cm3. Determine the length of the edges of a cube.
8. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
9. Rectangular cuboid The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
10. Cuboid Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
11. Pool The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
12. Cubes One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
13. Transforming cuboid Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
14. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
15. Cylinders Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
16. Tanks Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
17. Cone Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
18. Sandpile Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the san
19. Circular pool The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
20. Floating barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.

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