Question

Each edge of a cube is (4x10^2) mm long. Find the volume of the cube in m^3, giving your answer in standard form.

a) 64 m^3
b) 0.64 m^3
c) 0.0064 m^3
d) 6.4 m^3

Answer 1

The volume of the cube is 0.064 m^3, which is 6.4x10^-2 m^3 in standard form, corresponding to answer option c) 0.0064 m^3.

Step-by-step explanation:

The question asks to find the volume of a cube when the edge length is given as (4x102) mm. We know that the volume of a cube is calculated by cubing the length of one of its edges (V = a3). Since there are 103 mm in one meter (1 m = 103 mm), we need to convert the given edge length to meters before calculating the volume. The given edge length is 400 mm, which is 0.4 meters as there are 1000 mm in 1 m.

To calculate volume in meters cubed (m3), cube the edge length in meters:

V = (0.4 m)3
V = 0.064 m3

In standard form, this is 6.4x10-2 m3, which corresponds to answer option c) 0.0064 m3.