Volume + body volume - problems

1. Prism 4 sides
The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
2. Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
3. The diagram 2
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
4. Prism 4 sides
Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
5. 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.
6. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
7. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
8. 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.
9. 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.
10. 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?
11. 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.
12. Transforming cuboid
Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
13. Sphere
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
14. 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?
15. 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
16. 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.
17. Sand pile
Auto sprinkled with sand to 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 sand c
18. 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?
19. 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.
20. Rotation
Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.

Do you have an interesting mathematical problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.