Chapter 12.4, Problem 10PSB

Solution

a.

To calculate: The volume and the total area of the right cylinder ABCD

The volume and the total area of the right cylinder ABCD are $108\pi$ unit ${}^3$ and $90\pi$ unit ${}^2$ respectively.

Given:

The measures of the given lengths are as follows:

AB(h) = $12$

(Where, “h” is height)

AC(r) = $9$

(Where, “r” is radius)

Concept used:

Here, we are using the formula:

Area of cylinder = $2\pi r\left(r+h\right)$

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

Volume of cylinder = $\pi r^{2}h$

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

Calculation:

  

Here, Area of cylinder = $2\pi r\left(r+h\right)$

(Where, “r” is $4.5$ and “h” is $12$ )

➜ $2\pi \times 4.5\left(4.5+12\right)$

➜ $148.5\pi$

and, Volume of cylinder = $\pi r^{2}h$

(Where, “r” is $4.5$ and “h” is $12$ )

➜ $\pi \times {\left(4.5\right)}^2\times 12$

➜ $108\pi$

Conclusion: Hence, the volume and the total area of the right cylinder ABCD are $108\pi$ unit ${}^3$ and $90\pi$ unit ${}^2$ respectively.

b.

To calculate: The volume and the total area of the right cylinder

The volume and the total area of the right cylinder are $360\pi$ unit ${}^3$ and $156\pi$ unit ${}^2$

Given:

The measures of the given lengths are $6,6$ and $20$

Concept used:

Here, we are using the formula

Area of cylinder = $\frac{1}{2}\times 2\pi r\left(r+h\right)$

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

Volume of cylinder = $\frac{\pi }{2}\times r^2\times h$

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

Calculation:

Here, Area of cylinder = $\frac{1}{2}\times 2\pi r\left(r+h\right)$

(Where, “r” is $6$ and “h” is $20$ )

➜ $\pi r\left(r+h\right)$

➜ $6\pi \left(20\right)$

➜ $120\pi$

And, Volume of cylinder = $\frac{\pi }{2}\times r^2\times h$

(Where, “r” is $6$ and “h” is $20$ )

➜ $\frac{\pi }{2}\times {\left(6\right)}^2\times 20$

➜ $\frac{\pi }{2}\times 36\times 20$

➜ $360\pi$

Conclusion: Hence, the volume and the total area of the right cylinder are $360\pi$ unit ${}^3$ and $156\pi$ unit ${}^2$