What is the surface areo of the cone(hat) and what is the circumference of the base of the cone(hat)? the side of the cone has a angle 144' and a length of 25cm? 1) How do you find the radius?

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Assuming that you are cutting a sector out of a circle with radius 25 and central angle `144^@` and forming a cone with what is left.

The radius of the circle is the slant height of the cone (length of side) and equals 25. Then the arc length that is left is `216/360=3/5` of the circumference of the original circle. Since the circle had circumference `C=2pir=2pi(25)=50pi` we have the arc length `3/5*50pi=30pi` . This is the circumference of the base of the cone.

The circumference of the base of the cone is `C=2piR` where R is the radius of the cone. So `2piR=30pi==>R=15`

The radius of the base of the cone will be 15cm.

(The circumference of the base is `30pi "cm"` ; the surface area of the cone is the area of the original circle left after removing the sector. Then SA=`216/360pir^2=3/5pi(625)=375pi"cm"^2` )

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