^{2}where r is the radius of the sphere. If the sphere does not have an internal temperature gradient, then the time for it to cool to a certain temperature, t

_{2}, is inversely proportional to the surface area to volume ratio of the sphere, where the volume is V=4/3pi r

^{3}Thus, for two spheres or radii r

_{1}, r

_{2}, the cooling time for sphere 2, t

_{2}, can be calculated by the experimentally determined cooling time for sphere 1, t

_{1},: t

_{2}=t

_{1}(A

_{1}/V

_{1}/ A

_{2}/V

_{2}). Write and record a macro to calculate the cooling time of sphere 2 based on (1) the surface area of the sphere, (2) the volume of the sphere, and (3) the experimentally measured cooling time of a sphere of the same material: USE VBA a). First, do the calculation on the spreadsheet by creating a table and then filling in the numbers for a sphere of 0.005 m radius that cools in 2.3 s, and a sphere of the same material of 0.012 m radius. Use a

**Function macro**to calculate t

_{2}=t

_{1}(A

_{1}/V

_{1}/ A

_{2}/V

_{2}).

Sphere 1 | Sphere 2 | |

Radius (m) | 0.005 | 0.012 |

Cooling Time (s) | 2.3 |

**b) Write**a Macro (you may use a mix of record and write) that allows you to input the values for r

_{1}, r

_{2}, and t

_{1}using an InputBox, then fills in these values in the table, calculates t

_{2}, and then writes the result in the table.