The question asks for the definition of volume. We need to evaluate each option against the standard scientific definition of volume.
Correct Option: C) Space occupied by an object
The question asks for the SI unit of volume. To answer this, we need to recall the definitions of fundamental SI units and how derived units like volume are expressed in terms of these fundamental units.
Correct Option: B) Cubic meter
To find the volume of a cube, we need to know its side length. The formula for the volume of a cube is the cube of its side length.
Identify the given information: The side length of the cube is given as 3 meters.
Let \(s\) be the side length. \[ s = 3 \text{ meters} \]
Recall the formula for the volume of a cube: The volume (\(V\)) of a cube is calculated by cubing its side length.
\[ V = s^3 \]
Substitute the given side length into the formula:
\[ V = (3 \text{ meters})^3 \]
Calculate the volume:
\[ V = 3 \times 3 \times 3 \text{ cubic meters} \] \[ V = 9 \times 3 \text{ cubic meters} \] \[ V = 27 \text{ cubic meters} \]
Correct Option: D) 27 cubic meters
To find the volume of a rectangular prism, we use the formula: Volume = Length × Width × Height. We are given the length, width, and height, so we just need to substitute these values into the formula and calculate the result.
The volume \((V)\) of a rectangular prism is given by the product of its length, width, and height.
\[ V = L \times W \times H \]Since each dimension is in meters, the volume will be in cubic meters \((m^3)\).
Correct Option: B) 48 cubic meters
To determine the specific gravity of a solid object, we need a method that relates its weight in air to its weight when immersed in a fluid. Specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water at 4°C). Archimedes' principle directly deals with the buoyant force experienced by an object immersed in a fluid, which is crucial for this calculation.
Correct Option: A) Archimedes' principle is the fundamental principle used to determine the specific gravity of a solid object by measuring its weight in air and its apparent weight when immersed in a fluid (usually water).
The question asks to identify the correct statement about specific gravity. We need to understand the definition of specific gravity and its relationship with density, units, and dimensions.
C) It is the mass per unit volume of a substance relative to the mass per unit volume of water.
This statement accurately defines specific gravity. "Mass per unit volume" is the definition of density. So, specific gravity is the ratio of the density of a substance to the density of a reference substance (usually water). This makes option C correct.
While specific gravity is indeed a dimensionless quantity (as it is a ratio of two densities, and units cancel out), this statement alone is not the most complete or defining characteristic compared to option C. Option C provides the fundamental definition.
Kilograms per cubic meter (kg/m³) is the unit for density, not specific gravity. Since specific gravity is a ratio of two densities, its units cancel out, making it a dimensionless quantity. Therefore, this statement is incorrect.
Specific gravity is not the same as density. Density is an absolute measure of mass per unit volume (e.g., in kg/m³), while specific gravity is a relative measure, comparing a substance's density to a reference density. They are numerically equal only when the reference density is 1 (e.g., density in g/cm³ compared to water's density of 1 g/cm³), but conceptually and dimensionally, they are different. Therefore, this statement is incorrect.