Find the surface area of the cone. Use 3.14 for pi. The diameter is 8in and the height is 7in please help asap!! And thank you for your time. Ms.Sue?

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middleschool-teacher's profile pic

middleschool-teacher | Middle School Teacher | (Level 1) Adjunct Educator

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There are three measurements you need to calculate the surface area of a cone and they are: it's radius, height, and the slanted length.  The formula itself is SA (3.14)rs + (3.14)r2

Pi is abbreviated to just 3.14.  When you are calculating the cone's surface area, you are really adding the surface area of the cone "(3.14)rs" and the area of the circle "(3.14)r2".  r is 4 inches because r is radius which is one-half the length of the diameter.  When you see a slightly higher and smaller number right beside another number is is call an exponent.  The exponent, in this case 2, tells you how many times you multiply the base (the larger number to the left of the exponent) to itself.  So for example r2 here would be 4*4

In the end....SA = 87.92 + 50.24 = 138.16 square inches

steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

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One formula for the surface area of a cone is:

`S = pi*r^(2) + pi*r*l`  

Here:

S = surface area

r = radius = 4 in.

l = diagonal length = 7 in.

Plugging these values into the formula:

`S = pi*4^(2) + pi*4*7`

= 16pi + 28pi = 44pi = 138.16 square inches

alex1981's profile pic

alex1981 | eNotes Newbie

Posted on

The area of the cone is: 

`A=3.14*r*(r+sqrt(r^2+h^2))`

Here:  `r=4` ` `

`h=sqrt(7^2-4^2)=sqrt(33)`

`A=3.14*4*(4+sqrt(16+33))=3.14*4*11=132*3.14=414.48`  inches squared

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