Volume - practice for 14 year olds - page 39 of 40
Number of problems found: 787
- Cube in a sphere
The cube is inscribed in a sphere with a volume 7253 cm³. Determine the length of the edges of a cube. - Cuboid
Cuboid with edge a=6 cm and space diagonal u=31 cm has volume V=900 cm³. Calculate the length of the other edges. - Cubes
One cube is an inscribed sphere, and the other one is described. Calculate the difference of volumes of cubes if the difference of surfaces in 231 cm². - Cone A2V
The cone's surface in the plane is a circular arc with a central angle of 126° and area 415 cm². Calculate the volume of a cone.
- Axial section
The axial section of the cone is an equilateral triangle with an area 208 m². Calculate the volume of the cone. - Rotation
The right triangle with legs 11 cm and 18 cm rotates around the longer leg. Calculate the volume and surface area of the formed cone. - Hole
We will drill the cylinder shape hole in the cube's center with an edge 14 cm. The volume of the hole must be 27% of the cube. What should drill diameter be chosen? - Pool
The swimming pool is 10 m wide and 8 m long, and 153 cm deep. How many hectoliters of water are in it if the water is 30 cm below its upper edge? - Cone
The circular cone has height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane if solids have the same volume.
- Pool
If water flows into the pool by two inlets, fill the whole for 20 hours. The first inlet filled the pool 8 hour longer than the second. How long does the pool take to fill with two inlets separately? - Cube corners
From the cube of edge 5 cm, we cut off all vertices so that each cutting plane intersects the edges 1 cm from the nearest vertice. How many edges will this body have? - Sphere
The sphere's surface is 12100 cm², and the weight is 136 kg. What is its density? - Transforming cuboid
A cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length? - Pipes
The water pipe has a cross-section 1184 cm². An hour has passed 743 m³ of water. How much water flows through the pipe with cross-section 300 cm² per 6 hours if water flows at the same speed?
- Gold wire
From one gram of gold was pulled wire 1.4 km length. What is its diameter if the density of Au is ρ=19.5 g/cm³? - Diamond
Find the side of the diamond if its area is S = 490 cm² and one diagonal u2 = 39 cm. - Cone and cube
About what percentage has cone with base radius r larger volume than a same high cube with square base with edge length r? - Barrel of oil
The barrel of oil weighs 283 kg. When it molded 26% oil, it weighed 216 kg. What is the mass of the empty barrel? - Cylinder - basics
Cylinder with base radius r = 54 cm and height h=35 cm. Calculate: a) Area of the base
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