- A uniform cube Q and a uniform cube R have equal mass. Cube Q has greater side length. Which statement is correct?
Answer: Cube R is denser because the same mass occupies less volume.
This question examines density when cubes have equal mass but different side lengths and volumes. Density equals mass divided by volume (ρ = m/V), and cube volume equals side length cubed. Cube R has the same mass as cube Q but smaller side length (thus smaller volume), meaning R's matter is more concentrated and has higher density. Option A incorrectly suggests the larger cube is denser, which violates the inverse relationship between volume and density when mass is held constant. For equal-mass cubes, smaller side length always indicates greater density. - A cube of material M is cut into eight smaller cubes. Which statement about density is correct?
Answer: Each small cube has the same density as the original cube.
This question tests understanding of how cutting affects material density. Density is an intensive property that depends only on the material composition, not on the amount of material or object size. When a uniform cube is cut into smaller pieces, each piece retains the same density as the original because the ratio of mass to volume remains constant throughout the material. Option A incorrectly suggests that smaller size increases density, but density is independent of object size for uniform materials. Cutting, reshaping, or dividing uniform materials never changes their intrinsic density.
- Two identical containers are filled to the brim, one with liquid A and one with liquid B. The container with liquid B has less mass. Which is correct?
Answer: Liquid A is denser because equal volumes have greater mass.
This question applies density concepts to liquids using equal-volume containers with different masses. Density is mass per unit volume (ρ = m/V), so when volumes are identical, the liquid with greater mass has higher density. The container with liquid A has more mass than the container with liquid B at the same fill level, indicating that liquid A is denser than liquid B. Option A incorrectly claims liquid B is denser despite having less mass, which contradicts the density relationship. For equal volumes of liquids, greater mass always indicates higher density. - Two objects have equal volume. Object X has greater mass than object Y. Which statement about density is correct?
Answer: Object X is denser because it has more mass per unit volume.
This question tests density understanding when objects have equal volumes but different masses. Density is defined as mass per unit volume (ρ = m/V), so with identical volumes, the object with greater mass has higher density. Object X contains more mass than object Y in the same volume, indicating more matter per unit volume and higher density. Option A incorrectly states that the lighter object is denser, which directly contradicts the density formula. When volumes are equal, always identify which object has greater mass to determine higher density. - A sealed container C and sealed container D have the same mass. C has a smaller volume than D. Which statement about density is correct?
Answer: C is denser because the same mass is in less volume.
This question examines density when containers have equal mass but different volumes. Density is mass divided by volume (ρ = m/V), so when mass remains constant, smaller volume results in higher density. Container C has the same mass as D but occupies less space, meaning its contents are more concentrated or tightly packed. Option A incorrectly suggests that larger volume leads to higher density, which violates the inverse relationship between volume and density when mass is fixed. For equal-mass objects, smaller volume always indicates greater density. - A chunk of wax and a chunk of clay have equal mass. The wax chunk has larger volume. What follows?
Answer: Clay is denser because the same mass occupies less volume.
This question examines density when materials have equal mass but different volumes. Density is mass per unit volume (ρ = m/V), so when mass remains constant, the material with smaller volume has higher density. The clay chunk has the same mass as the wax but occupies less space, meaning clay's matter is more tightly packed and has higher density. Option A incorrectly suggests wax is denser because it takes up more space, which contradicts the inverse relationship between volume and density. For equal-mass materials, smaller volume always indicates greater density.
- A solid object is drilled to remove some material, decreasing its mass and volume proportionally. Which statement about density is correct?
Answer: Density stays the same because the material is unchanged.
This question examines how proportional removal of material affects density. Density is mass per unit volume (ρ = m/V), and when mass and volume decrease by the same proportion, their ratio remains constant. If drilling removes material uniformly, both mass and volume decrease proportionally, keeping density unchanged because the material composition remains the same. Option A incorrectly suggests density increases when mass decreases, ignoring that volume also decreases proportionally. When mass and volume change proportionally for the same material, density remains constant.
- Two sealed bottles have equal volume. Bottle G has greater mass than bottle H. What can be inferred about their average densities?
Answer: Bottle G has greater average density than bottle H.
This question applies density concepts to sealed containers with equal volumes but different masses. Density is mass per unit volume (ρ = m/V), so when volumes are identical, the container with greater mass has higher average density. Bottle G contains more mass than bottle H in the same volume, indicating that G's contents are more densely packed. Option A incorrectly claims the lighter bottle is denser, which contradicts the fundamental relationship between mass and density. When comparing equal-volume sealed containers, greater mass always indicates higher average density. - A uniform material is molded into a new shape without adding or removing any material. Which statement about its density is correct?
Answer: Density stays the same because mass and volume stay the same.
This question tests understanding of density as an intrinsic material property during reshaping. Density is a characteristic property that depends only on material composition and structure, not on shape or external form. When a uniform material is molded into a new shape without adding or removing material, both mass and volume remain constant, so density stays the same. Option A incorrectly suggests density changes due to shape changes, but shape doesn't affect the fundamental mass-to-volume ratio. Reshaping objects never changes their intrinsic material density.
- Two objects have equal mass. Object C has greater volume than object D. Which statement about their densities is correct?
Answer: D is denser because the same mass is in less volume.
This question examines density when objects have equal mass but different volumes. Density equals mass divided by volume (ρ = m/V), so when mass is constant, the object with smaller volume has higher density. Object D has the same mass as object C but occupies less space, meaning D's matter is more tightly packed and has higher density. Option A incorrectly suggests the larger object is denser, which violates the inverse relationship between volume and density when mass is held constant. For equal-mass objects, smaller volume always indicates greater density. - A solid cube and a solid sphere have the same mass. The cube has greater volume than the sphere. Which statement is supported?
Answer: The sphere is denser because the same mass occupies less volume.
This question examines density when objects have equal mass but different volumes. Density equals mass divided by volume (ρ = m/V), so when mass is constant, the object with smaller volume has higher density. The sphere has the same mass as the cube but occupies less volume, meaning the sphere's matter is more concentrated and has higher density. Option A incorrectly suggests the cube is denser because of its shape, but density depends on mass-to-volume ratio, not shape. For equal-mass objects, smaller volume always indicates greater density.
- Two sealed cubes have the same outer volume. Cube U contains a solid metal core plus empty space; cube V is completely filled with a less-dense foam. Both cubes have the same total mass. Which inference is supported?
Answer: The cubes have equal average density because they have equal mass and equal outer volume.
This question explores how different internal structures can yield the same average density. Density is mass per unit volume (ρ = m/V), and average density uses total mass and total outer volume regardless of internal composition. Both cubes have equal mass and equal outer volume, so their average densities are identical: ρ_avg = m/V for both. Cube U achieves this density with a dense metal core plus empty space, while cube V uses uniformly distributed foam throughout. Choice A incorrectly assumes metal content guarantees higher average density without considering the compensating effect of empty space. The key insight is that different internal arrangements (concentrated dense material vs. distributed less-dense material) can produce the same average density when total mass and volume are equal.
- A wooden block and a plastic block have equal volumes. The plastic block's mass is smaller. What can be concluded?
Answer: Wood has greater density because it has greater mass for the same volume.
This problem tests understanding of density relationships when volumes are equal but masses differ. Density is defined as mass per unit volume (ρ = m/V), so with equal volumes, density is directly proportional to mass. The wooden block has greater mass than the plastic block for the same volume, making wood denser in this case. The internal structure of wood must have more tightly packed molecules or heavier atoms than the plastic, resulting in more mass in the same space. Choice A incorrectly states that smaller mass means greater density. When comparing equal volumes, always remember that greater mass means greater density.
- A sphere of foam and a sphere of rubber have equal mass. The foam sphere has larger radius. Which is correct?
Answer: Rubber is denser because the same mass occupies less volume.
This question examines density when spheres have equal mass but different volumes due to different radii. Density equals mass divided by volume (ρ = m/V), so when mass is constant, the sphere with smaller volume has higher density. The rubber sphere has the same mass as the foam sphere but smaller radius (thus smaller volume), meaning rubber's matter is more tightly packed and has higher density. Option A incorrectly suggests the larger foam sphere is denser, which violates the inverse relationship between volume and density. For equal-mass objects, smaller volume always indicates greater density.
- Two samples of the same substance are at the same temperature. Sample 1 has greater mass and greater volume than sample 2. What follows?
Answer: Both samples have the same density.
This question tests understanding of density as an intrinsic material property. Density is a characteristic property of substances that remains constant regardless of sample size when temperature and pressure are constant. Since both samples are the same substance at the same temperature, they have identical density even though one sample has greater mass and volume than the other. Option A incorrectly suggests that greater mass leads to greater density, ignoring that volume also increases proportionally. For the same substance under identical conditions, density is always constant regardless of sample size.
- A solid ball and a hollow ball have the same outer radius. The solid ball has greater mass. What can be inferred?
Answer: The solid ball has greater average density.
This question examines density comparison between solid and hollow objects with the same outer dimensions. Density is mass per unit volume (ρ=m/V), and with equal outer radii, both balls have the same external volume. The solid ball has greater mass because it contains material throughout its volume, while the hollow ball contains air, resulting in higher average density for the solid ball. Option A incorrectly suggests the hollow ball is denser because it contains air, but air has much lower density than solid materials. Solid objects are always denser than hollow versions with the same outer dimensions. - A solid object E and a solid object F have equal volumes. E has less mass than F. Which statement is correct?
Answer: F is denser because it has more mass for the same volume.
This question tests density understanding when objects have equal volumes but different masses. Density is defined as mass per unit volume (ρ = m/V), so with identical volumes, the object with greater mass has higher density. Object F has more mass than E in the same space, indicating more concentrated matter and higher density. Option A incorrectly states that the lighter object is denser, which directly contradicts the density formula. When volumes are equal, always compare masses to determine which object has higher density. - A sealed container of fixed volume is filled with beads. Container 1 has more beads and greater mass than container 2. Which inference is supported?
Answer: Container 1 has greater average density because it has greater mass in the same volume.
This question applies density concepts to containers with different amounts of the same type of objects. Density is mass per unit volume (ρ = m/V), and when volumes are equal, the container with greater mass has higher average density. Container 1 has more beads and greater total mass than container 2 in the same volume, resulting in higher average density due to more matter packed into the same space. Option A incorrectly suggests fewer beads lead to higher density, which contradicts the mass-density relationship. More objects in the same volume always produces higher average density.
- Two identical-volume spheres are made of different materials. Sphere L has greater mass than sphere M. What can be concluded?
Answer: Sphere L is denser because it has greater mass for the same volume.
This question tests density understanding when spheres have equal volumes but different masses. Density is defined as mass per unit volume (ρ = m/V), so with identical volumes, the sphere with greater mass has higher density. Sphere L contains more mass than sphere M in the same space, indicating denser material with atoms packed more tightly together. Option A incorrectly claims the lighter sphere is denser, which directly contradicts the density formula. When comparing equal-volume objects made of different materials, greater mass always indicates higher density. - Two uniform samples are made of different materials. Sample A has both greater mass and greater volume than sample B. Which inference is supported?
Answer: No definite density comparison can be made from this information alone.
This question examines density comparison when both mass and volume differ between samples. Density equals mass divided by volume (ρ = m/V), and without knowing the specific ratios of mass and volume changes, no definitive density comparison can be made. Sample A could have higher, lower, or equal density compared to sample B depending on whether mass increased more, less, or proportionally compared to volume. Option A incorrectly assumes greater mass automatically means greater density, ignoring the volume component. When both mass and volume differ, density comparison requires knowing the specific mass-to-volume ratios.
