Practice problems of the volume - last page
Volume is the measure of the space that a body fills or occupies. The basic SI unit of volume is the cubic meter. It is the volume of a cube with an edge of one meter, i.e., 1 m x 1 m x 1 m. Significant another unit is 1 l (one liter), 1 m3 = 1000 l applies. One hectoliter (1 hl) is 100 liters.Volume is always the third power of length. Or volume = area times length. For example, the volume of the cube is a3, and the prism's volume is S*h (the area of the base times the height). The volume of rotating bodies (sphere, cone) can be derived in high school by integration. The pyramid's volume is always 1/3 of the prism's volume. We calculate the volume of the truncated bodies either with a formula or simply by subtracting the volumes of the two bodies.
Number of problems found: 2352
- Density - simple example
Material of density of 1189 kg/m³ occupies a container volume of 64 cm³. What is its mass? - Floating barrel
The barrel (cylinder shape) floats on water, the top of the 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. - Cone in cylinder
The cylinder is an inscribed cone. Find the ratio of the volume of the cone and cylinder. Please write the ratio as a decimal number and as a percentage. - Cone in cube
The cube is an inscribed cone. Determine the ratio of the volume of cone and cube. Please write the ratio as a decimal number and as a percentage.
- Aquarium
An aquarium is a rectangular box with a square base containing 76 liters of water. The length of the base edge is 42 cm. To what height does the water level rise? - Hollow sphere
Calculate the weight of a hollow stříbrné sphere (density 10.5 g/cm³) if the vnitřní diameter is 15 cm and wall thickness is 1 mm. - Cube in ball
The cube is inscribed into the sphere of radius 181 dm. How many percent is the volume of cube of the volume of the sphere? - Plasticine ball
Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. These balls are - Cu thief
The thief stole 142 meters copper wire with a cross-section area of $s mm². Calculate how much money gets in the scrap redemption if redeemed copper for 5.3 Eur/kg. The density of copper is 8.96 t/m³.
- Sandpile
Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the base's circumference and the length of both sides of the cone (over the top). What is the sand cone's volume if t - Engineer Kažimír
The TV show example beautifully illustrates the difference between politicians-demagogues and reasonable people with at least primary education. Engineer Kažimír says that during their tenure, there was a large decline in the price of natural gas. The pri - Eiffel Tower
Eiffel Tower in Paris is 300 meters high and is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material if it weighs 1.8 kg?
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