Chapter ISG, Problem 3.1.2.2P

To determine

To form a function for the lateral area

Answer to Problem 3.1.2.2P

The function is, $L(x)=62.832x$

Explanation of Solution

Given:

Slant height (l) is constant, which is 20 inches.

Radius (x) can vary.

Value of $\pi$ is3.1416

Formula Used:

Lateral area of cone is,

  $L=\pi rl$

Calculation:

Substituting the value in the lateral area formula,

  $L(x)=3.1416\times x\times 20$

On solving,

  $L(x)=62.832x$

Conclusion:The function for lateral area of conical hat is, $L(x)=62.832x$

To determine

To graph the lateral function. Calculate the amount of cloth required for radius 3.5 inches

Answer to Problem 3.1.2.2P

Amount of cloth needed for the hat with radius 3.5 is 219.912 square inches

Explanation of Solution

Given:

The constraints for the lateral function are, $-10\le x\le 10$

and $-1000\le y\le 1000$

Lateral function is $L(x)=62.832x$

Radius is 219.912 inches.

Graph:

  

Calculation:

For the amount of cloth required.

Substituting the value in the lateral function,

  $L(3.5)=62.832\times 3.5$

On solving,

  $L(3.5)=219.912$

Conclusion:

Amount of cloth needed for the hat with radius 3.5 is 219.912 square inches