Chapter 12.6, Problem 19HP

To determine

Calculate the surface area of cylinder having diameter of 10.2 ft and height of 14.6 ft.

Answer to Problem 19HP

Surface area of cylinder= $631.26f{t}^2$

Prism with side of 10.25 ft is having same surface area as that of cylinder.

Explanation of Solution

Given:

Diameter=10.2ft ; radius=5.1ft

Height = 14.6 ft

Calculations:

Here, we have to calculate lateral and surface area of cylinder.

We know that, surface area of cylinder is calculated as,

  $Surfacearea=2\pi r^2+2\pi rh$

Where, $r$ is the radius of cylinder h is the height of cylinder

Putting values in equation, we get

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times \pi \times {5.1}^2)+(2\times \pi \times 5.1\times 14.6)\\ =163.42+467.84\\ =631.26f{t}^2\end{array}$

Surface area of a cube can be calculated as,

  $Surfaceareaofcube=6a^2$

Where, a = side of cube

Surface area of Prism is having same surface area of cylinder.

Therefore,

  $\begin{array}{l}Surfaceareaofcube=6a^2\\ 631.26=6a^2\\ a^2=\frac{631.26}{6}\\ a^2=105.21\\ a=\sqrt{105.21}\\ a=10.25ft\end{array}$

Thus, prism having side 0f 10.25 ft is having same surface area as that of cylinder.

Conclusion:

Therefore, we are able to calculate surface area of cylinder and create its equivalent prism.