Answer:
<em>The total surface area of the seven little spheres is 1.91 times the total surface area of the bigger sphere.</em>
Explanation:
<u>Volume of a Sphere</u>
The volume of a sphere of radius r is given by:

The volume of each little sphere is:


When the seven little spheres coalesce, they form a single bigger sphere of volume:

Knowing the volume, we can find the radius rb by solving the formula for r:

Multiplying by 3:

Dividing by 4π:

Taking the cubic root:
![\displaystyle r_b=\sqrt[3]{\frac{3V_b}{4\cdot \pi}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r_b%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3V_b%7D%7B4%5Ccdot%20%5Cpi%7D%7D)
Substituting:
![\displaystyle r_b=\sqrt[3]{\frac{3*234.57}{4\cdot \pi}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20r_b%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B3%2A234.57%7D%7B4%5Ccdot%20%5Cpi%7D%7D)

The surface area of the seven little spheres is:

The surface area of the bigger sphere is:

The ratio between them is:

The total surface area of the seven little spheres is 1.91 times the total surface area of the bigger sphere.