The surface area of the outside of the block is determined by the difference of cube and cylinder.
The surface area of cylinder is,
![S_c=\text{ 2}\Pi rh+2\Pi(r^2)](https://img.qammunity.org/2023/formulas/mathematics/college/221by2mbxuscdb1pw8ft5ob36foyj9b06c.png)
The radius is 2 ft and height is 6 ft.
![S_c=2\Pi(2*6+2^2)](https://img.qammunity.org/2023/formulas/mathematics/college/s4f98weaa8kwubbx5898kp3si5y8erhtgz.png)
![S_c=\text{ 2}*3.14*(12+4)](https://img.qammunity.org/2023/formulas/mathematics/college/5q9e2hijy43631gz3g7alza8m9ozvbtx73.png)
![S_c=100.48ft^{2^{}}](https://img.qammunity.org/2023/formulas/mathematics/college/r3bgzyqsdq21lps2e33hj2kzt8wktm9csi.png)
The surface area of cube is,
![S_a=6s^2](https://img.qammunity.org/2023/formulas/mathematics/college/wkw74wvjzarm14fn32ktq6ulw4kega5wsi.png)
The sidde of cube is 6 ft.
![S_a=\text{ 6}*6^2](https://img.qammunity.org/2023/formulas/mathematics/college/18bh4yc4fnxda5fr8s4k0azbaaj5hr7av8.png)
![S_a=216ft^2](https://img.qammunity.org/2023/formulas/mathematics/college/lmwedf4j87v2942jn5vfzdd5mrk5k0ik9i.png)
The surface area of the outside of the block is,
![S=S_a-S_c](https://img.qammunity.org/2023/formulas/mathematics/college/n626ik4e3ews9sgtx2jccahluip4ptifyh.png)
![S=\text{ 216-100.48}](https://img.qammunity.org/2023/formulas/mathematics/college/5zhuaikn3wkgjo3434u2cnqsnsutooyo7f.png)
![S=115.52ft^2](https://img.qammunity.org/2023/formulas/mathematics/college/z6zjyqnwinxu0lp9o7whjdooxh3o2wfu7y.png)