Chapter 12, Problem 11RP

a.

To determine

To calculate: The total surface area of hemisphere

Answer to Problem 11RP

The total surface area of hemisphere is $30\pi$

Explanation of Solution

Given:

The radius is $5$

Concept used:

Total surface area of hemisphere = $\pi r^2+\pi r$

(Where “ r ” is radius)

Calculation:

Here, Total surface area of hemisphere = $\pi r^2+\pi r$

(Where “ r ” is radius)

  → $\pi r\left(r+1\right)$

  → $5\pi \left(6\right)$

  → $30\pi$

Conclusion: Hence, the total surface area of hemisphere is $30\pi$

b.

To determine

To calculate: The total surface area of the half cone

Answer to Problem 11RP

The total surface area of the half cone is $45\pi +60$

Explanation of Solution

Given:

Radius = $5$

Slant height = $13$

Concept used:

Here, we are using the formula:

Total surface area of half cone = $\frac{1}{2}\left(\pi rl+\pi r^2\right)+\frac{1}{2}\times b\times h$

(Where, “ r ” is radius, “ b ” is base and “ h ” is height)

Calculation:

Here, total surface area of half cone = $\frac{1}{2}\left(\pi rl+\pi r^2\right)+\frac{1}{2}\times b\times h$

(Where, “ r ” is radius, “ b ” is base and “ h ” is height)

  → $\frac{1}{2}\left(\pi \times 5\times 13+\pi \times 25\right)+\frac{1}{2}\times 10\times \left(\sqrt{169-25}\right)$

  → $\frac{1}{2}\left(65\pi +25\pi \right)+50$

  → $45\pi +60$

Conclusion: Hence, the total surface area of the half cone is $45\pi +60$