# Body volume - high school - examples

1. Sphere floating
Will float a hollow iron ball with an outer diameter d1 = 20cm and an inside diameter d2 = 19cm in the water? The iron density is 7.8 g/cm 3. (Instructions: Calculate the average sphere density and compare with the density of the water. )
2. 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
3. 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.
4. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
5. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
6. 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.
7. 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.
8. 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.
9. 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?
10. 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?
11. Cone
Calculate volume and surface area of ​​the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°.
12. 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?
13. Cube zoom
How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
14. 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
15. 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?
16. Rotation
Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
17. Prism X
The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
18. Plastic pipe
Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m3.
19. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
20. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.

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