Dan has a conical lamp shade with an altitude of 6 inches and a diameter of 12 inches. How much material is needed to make the lampshade

226.22 in^2

Step-by-step explanation:

Given data

Height l= 6in

Diameter= 12in

Radius= 12/2= 6in

The expression for the total surface area of a cone is given as

TSA= πrl+πr^2

substitute

TSA= 3.142*6*6+3.142*6^2

TSA= 113.112+113.112

TSA= 226.22 in^2

Hence the TSA is 226.22 in^2

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: