Body volume - examples
- Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
- Volume of cone
Find the volume of a right circular cone-shaped building with a height of 9 cm and a radius base of 7 cm.
- Annual rainfall
The average annual rainfall is 686 mm. How many liters will fall on the 1-hectare field?
- Water tank
A 288 hectoliter of water was poured into the tank with dimensions 12 m and 6 m bottom and 2 m depth. What part of the volume of the tank water occupied? Calculate the surface of tank wetted with water.
- The coil
How many ropes (the diameter 8 mm) fit on the coil (threads are wrapped close together) The coil has dimension: the inner diameter 400mm, the outside diameter 800mm and the length of the coil is 470mm
- Cylindrical container
An open-topped cylindrical container has a volume of V = 3140 cm3. Find the cylinder dimensions (radius of base r, height v) so that the least material is needed to form the container.
- Cube in a sphere
The cube is inscribed in a sphere with volume 6598 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is equilateral triangle with area 300 m2. Calculate volume of the cone.
Cuboid with edge a=14 cm and body diagonal u=42 cm has volume V=10976 cm3. Calculate the length of the other edges.
The cuboid has a surface area 3380 cm2, the length of its edges are in the ratio 4:3:1. Calculate the volume of the cuboid.
The swimming pool is 4 m wide and 20 m long and 156 cm deep. How many hectoliters of water is in it, if the water is 9 cm below its upper edge.
- 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.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
- Transforming cuboid
Cuboid with dimensions 5 cm, 14 and 17 cm is converted into a cube with the same volume. What is its edge length?
The cube has area of base 400 mm2. Calculate the edge length, volume and area of its surface.
Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much?
Fire tank has cuboid shape with a rectangular floor measuring 14 m × 12.8 m. Water depth is 1.8 m. Water was pumped from the tank into barrels with a capacity of 4.4 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wri
Annual rainfall in our country are an average of 865 mm. How many m3 of water rains on average per hectare?
- Spherical cap
From the sphere of radius 12 was truncated spherical cap. Its height is 4. What part of the volume is spherical cap from whole sphere?