Final answer:
The radius of a 7.64 g sphere with a density of 0.14 g/cm³ is not directly given by any of the options a through d, as finding the radius involves dividing the mass by the density to get the volume, and then solving for the radius using the volume formula for a sphere.
Step-by-step explanation:
To find the radius of a sphere from mass and density, we need to use the formula for volume and density. The density ρ is mass m divided by volume V, so ρ = m/V. The volume of a sphere is given by V = (4/3)πr3, where r is the radius. For a sphere with a density ρ of 0.14 g/cm3 and a mass m of 7.64 g, we can set up the equation as follows: 0.14 g/cm3 = 7.64 g / ((4/3)πr3). To isolate r, we would rearrange the equation to solve for r3 and then take the cube root. None of the provided options a) through d) correspond to this process, since they involve simple division or square roots, not cubic roots. Calculating correctly, we first divide 7.64 g by 0.14 g/cm3 to get the volume in cubic centimeters, and then solve for the radius using the formula V = (4/3)πr3.