# Body volume - 9th grade (14y) - 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. Space diagonal The space diagonal of a cube is 129.91 mm. Find the lateral area, surface area and the volume of the cube.
3. 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
4. Right pyramid A right pyramid on a base 4 cm square has a slant edge of 6 cm. Calculate the volume of the pyramid.
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 9067 cm3. Determine the length of the edges of a cube.
7. Axial section Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
8. 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.
9. 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?
10. 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.
11. 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?
12. 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.
13. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
14. Cylinders Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. 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 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°.
17. Spherical cap From the sphere of radius 13 was truncated spherical cap. Its height is 6. What part of the volume is spherical cap from whole sphere?
18. Cube zoom How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
19. 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
20. Lathe From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?

Do you have an interesting mathematical word 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 the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...