# Body volume - 8th grade (13y) - math problems

1. The cylinder 2 Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
2. Three glasses Three glasses of different colors have different volumes. Red 1.5 liter is filled from 2/5, blue 3/4 liter is filled from 1/3, and the third green 1.2 liter is empty. Pour green glass 1/4 of the contents from the red glass and 2/5 of the content from the b
3. Wood prisms How many weight 25 prisms with dimensions 8x8x200 cm? 1 cubic meter of wood weighs 800 kg.
4. Cube in a sphere The cube is inscribed in a sphere with volume 9067 cm3. Determine the length of the edges of a cube.
5. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
6. 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.
7. 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?
8. 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.
9. Cone A2V Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
10. Tereza The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
11. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
12. 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?
13. 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
14. Cone Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
15. Spherical cap From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere?
16. Cube zoom How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
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. Lathe From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
19. Circular pool The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The 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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