Chapter 12.3, Problem 27WE

a.

To determine

To describe the solid and find its volume

Answer to Problem 27WE

The solid is cylinder when rotated and volume of the solid is $602.88$ cubic units

Explanation of Solution

Given: Consider thegiven information,

ABCD is a rectangle and it is rotated in space about $\overline{AB}$

AB = 10units

AD = 6units

Formula Used:

Volume = $2\pi rh+2\pi r^2$

Calculation: Consider the given information the formula is,

By rotating $\overline{AB}$ cylinder is formed.

Volume $=(2\times 3.14\times 6\times 10)+(2\times 3.14\times 36)$

  $=602.88$ cubic units

Conclusion:

The solid is cylinder when rotated volume of the solid is $602.88$ cubic units

b.

To determine

To describe the part(a) solid and find its volume

Answer to Problem 27WE

The solid is cylinder when rotated and volume of the solid is $1004.48$ cubic units

Explanation of Solution

Given: Consider thegiven information,

ABCD is a rectangle and it is rotated in space about $\overline{AD}$

AB = 10 units

AD = 6units

Formula Used:

Volume = $2\pi rh+2\pi r^2$

Calculation: Consider the given information the formula is,

By rotating $\overline{AD}$ cylinder is formed.

Volume $=(2\times 3.14\times 6\times 10)+(2\times 3.14\times 100)$

  $=1004.48$ cubic units

Conclusion:

The solid is cylinder when rotated volume of the solid is $1004.48$ cubic units