Practice problems of the volume - page 34 of 118
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: 2351
- Diameter 46661
The granite ball has a diameter of 80 cm. The mass of 1m³ of granite is 2900 kg. What is the mass of the ball? - Triangular 46641
The regular triangular pyramid ABCDV has a base edge length of 8 cm and a height of 7 cm. Calculate the pyramid's surface area and volume. - Regular square prism
The volume of a regular square prism is 192 cm³. The size of its base edge and the body height is 1:3. Calculate the surface of the prism. - Increase 46473
He enlarges the side of the 8 cm long cube by 20%. How much will its volume increase compare to the original cube?
- Plasticine 46461
How many g of plasticine do we need to model a cube with an edge of 150 mm if 1 cm³ weighs 2.1 g? - Quadrilateral 46431
Calculate the volume V and the surface S of a regular quadrilateral pyramid, the base edge and height of which are the same size as the edge of a cube with a volume V1 = 27m3 - Determine 46401
The volume of the sphere is 20% larger than the volume of the cone. Find its surface if the volume of the cone is 320 cm³. - Calculate 46381
Calculate the volume of the two pots and compare them. The first pot is 40cm high, and the diameter of its bottom is 24cm. The second pot is 24cm tall, and the diameter of its base is 40cm. - An architect 2
An architect is designing a house. He wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. The architect doubles all three dimensions to create the den. Does that mean the den will have double the volume of the bedroom? First, find the volume
- Cylinder from paper
From a rectangle measuring 20 x 30 cm, we roll a cylinder with a height of 30 cm. Find its volume and surface. - Instructions 46331
According to the instructions, you need to add two and a half scoops of ecological cleaning agent to 10 liters of water. The measuring cup is a cap with a volume of 50 ml. Determine the ratio in which this agent is mixed with water - The volleyball ball
The volleyball ball can have a circumference of at least 650 max 750 mm after inflation. What air volume can this ball hold if its circumference is the average of the minimum and maximum inflation of the ball? - Measuring 46271
Calculate the weight of a block measuring 15 cm, 7.5 cm, and 10 cm made of a) oak wood (ρ = 800 kg/m³), b) spruce wood (ρ = 550 kg/m³). - Length 46191
We poured 12 l of water into a cube with an edge length of 30 cm. How high is the water level?
- The solar
The solar heating tank has the shape of a rotating cylinder. When the tank is in a horizontal position, the water in the tank wets 4/5 of each tank base. If we place the tank in a vertical position, the water in the tank will reach up to 1.2 m. Calculate - Cylinder 46101
Barell has a cylinder shape, a volume of 130 l, and a base radius of 30 cm. What is the height of the barrel? - The vase
The vase has the shape of a cylinder with a diameter of 1.2 dm. From the upper edge to the water level is 20 cm, and the water depth is 35 cm. How much ml of water would fit in a vase if it was filled to the brim? - Calculate 45991
Calculate the radius of a sphere with the same volume as a cone with a radius of 5cm and a height of 7cm. - A recipe
A recipe requires 3/4 cups of milk. Paula is making 1/2 of the recipe. How many cups will Paula use?
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