Chapter 10.5, Problem 21E

(a)

To determine

To find the surface area.

Answer to Problem 21E

  $4\pi h^2$

Explanation of Solution

Given Information: Cylinder $Diameter=2\times Height$ , $Diameter=2\times Radius$ and $\pi =\frac{22}{7}$ .

  $2\times Radius=2\times Height$ So, Radius = Height

Formula Used:

Surface Area of Cylinder = $2\pi \times radius(height+radius)$

Calculation:

Radius = h, Height = h and $\pi =\frac{22}{7}$ .

Surface Area of Cylinder = $2\pi \times radius(height+radius)$

Put the value of Radius and Height to find Surface Area of Solid

Surface Area of Cylinder = $2\pi \times h(h+h)$

So,

Surface Area of Cylinder = $2\pi \times h(2h)$

Hence,

Surface Area of Solid = $4\pi h^2$

(b)

To determine

To find the radius and height.

Answer to Problem 21E

Height = 4 units and Radius = 4 units

Explanation of Solution

Given Information: Surface Area of Cylinder = $64\pi$

Cylinder $Diameter=2\times Height$ , $Diameter=2\times Radius$ and $\pi =\frac{22}{7}$ .

  $2\times Radius=2\times Height$ So, Radius = Height

Formula Used:

Surface Area of Cylinder = Compare both Surface Area

Calculation:

Radius = h, Height = h.

Already Solve,

Surface Area of Cylinder= $4\pi h^2$

Now compare both Surface Area,

  $64\pi$ = $4\pi h^2$

  $h^2=\frac{64}{4}$

  $h^2=16$

  $h=4$ unit

As,

Radius = Height

So,

Radius = 4 unit