Body volume - 9th grade (14y) - examples
- Square prism
Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms.
- Cube, cuboid, and sphere
Volumes of a cube and a cuboid are in ratio 3: 2. Volumes of sphere and cuboid are in ratio 1: 3. In what ratio are the volumes of cube, cuboid, and sphere?
- Inscribed sphere
How many percents of the cube volume takes the sphere inscribed into it?
- Cube in a sphere
The cube is inscribed in a sphere with volume 5951 cm3. Determine the length of the edges of a cube.
- Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
Cuboid with edge a=23 cm and body diagonal u=41 cm has volume V=13248 cm3. Calculate the length of the other edges.
The swimming pool is 10 m wide and 22 m long and 191 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 dm2. 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 254 cm2.
- Transforming cuboid
Cuboid with dimensions 10 cm, 17 and 17 cm is converted into a cube with the same volume. What is its edge length?
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
Area of the side of two cylinders is same rectangle of 12 mm × 19 mm. Which cylinder has a larger volume and by how much?
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
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°.
- 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?
- 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
- Cube zoom
How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
- 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.