Chapter 12.3, Problem 28WE

a.

To determine

To determine the volume and lateral area of the cone

Answer to Problem 28WE

The volume and lateral area of the cone is $37.68$ cubic units and $47.1$ sq. units

Explanation of Solution

Given: Consider thegiven information,

The segment is rotated about the x-axis forming the lateral surface of the cone.

Radius of cone = 3 units

Height of cone = 4 units

  $\pi \approx 3.14$

Formula Used:

Volume = $\frac{1}{3}\pi r^{2}h$

Lateral area = $\pi r\sqrt{r^2+h^2}$

Calculation: Consider the given information the formula is,

Volume = $\frac{1}{3}\times 3.14\times {(3)}^2\times 4$

  $=37.68$ cubic units

Lateral area = $3.14\times 3\times \sqrt{3^2+4^2}$

  $=47.1$ sq. units

Conclusion:

The volume and lateral area of the cone is $37.68$ cubic units and $47.1$ sq. units

b.

To determine

To determine the volume and lateral area of the cone

Answer to Problem 28WE

The volume and lateral area of the cone is $62.8$ cubic units and $50.24$ sq. units

Explanation of Solution

Given: Consider thegiven information,

The segment is rotated about the y-axis forming the lateral surface of the cone.

Radius of cone = 4units

Height of cone = 3units

  $\pi \approx 3.14$

Formula Used:

Volume = $\frac{1}{3}\pi r^{2}h$

Lateral area = $\pi r\sqrt{r^2+h^2}$

Calculation: Consider the given information the formula is,

Volume = $\frac{1}{3}\times 3.14\times {(4)}^2\times 3$

  $=62.8$ cubic units

Lateral area = $3.14\times 4\times \sqrt{4^2+3^2}$

  $=50.24$ sq. units

Conclusion:

The volume and lateral area of the prism is $62.8$ cubic units and $50.24$ sq. units

c.

To determine

Are the parts (a) and (b) the same

Answer to Problem 28WE

No the parts (a) and (b) the same

Explanation of Solution

Given: Consider thegiven information,

The segment is rotated about the x-axis forming the lateral surface of the cone.

Radius of cone = 3units

Height of cone = 4units

  $\pi \approx 3.14$

The parts (a) and (b) are not same because the axis of rotation are different.