### A hemisphere depression is cut out from one face of a cubical wooden block of length 'l' such that the diameter of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid.

**Answer:**

l^{2} |

4 |

**Step by Step Explanation:**

- Let us consider
**d**be the diameter of hemisphere and**l**be the edge of the cube.

Here, it is given that the diameter of the hemisphere is equal to the edge of the cube.

So, the diameter of the hemisphere**d**=**l**. Where, the edge of the cube =**l**. - Now,

The total surface area of the cube after hemispherical depression = The total surface area of the cube - The base area of the hemisphere + The curved surface area of the hemisphere = 6l ^{2}- πr^{2}+ 2πr^{2}= 6l ^{2}+ πr^{2}= 6l ^{2}+ π× (l/2)^{2}= 6l ^{2}+π l ^{2}4 =

(24 + π) sq.unitsl ^{2}4 - Thus, the total surface area of the cube after hemispherical depression is

(24 + π) sq.units.l ^{2}4