SOLUTION: How find the surface area and volume of a conical shape? https://www.flickr.com/photos/123400688@N08/13931846543/in/photostream/ The answer at the back of the book is: 603cm

Algebra ->  Surface-area -> SOLUTION: How find the surface area and volume of a conical shape? https://www.flickr.com/photos/123400688@N08/13931846543/in/photostream/ The answer at the back of the book is: 603cm      Log On


   

Question 864906: How find the surface area and volume of a conical shape?
https://www.flickr.com/photos/123400688@N08/13931846543/in/photostream/
The answer at the back of the book is:
603cm^3 and 377 cm^2
Please give me detailed explanation and solution.Please help me.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The picture gives you slant height and diameter. If s is slant height, d is diameter, r is radius, the if you lookup the formula for surface area of a cone using your Geometry book, this is pi%2Ar%2As; which EXCLUDES the area of the circular base.

Your picture is of two such cones sharing a circular base, so for your picutre, surface area is 2%2Ar%2As%2A%28pi%29
highlight%282%2A%2812%2F2%2910%2A%28pi%29%29

Formula for volume of a cone is v=%281%2F3%29pi%2Ax%2Ar%5E2; just be aware, you have two of these stuck together in your picture. You can find h using pythagorean theorem. h%5E2=x%5E2%2B%28d%2F2%29%5E2; and you already have d=12, h=10, and you can find x which is the HEIGHT of each cone, meaning from center of base to the cone tip. Do NOT confuse this height with "SLANT HEIGHT".
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Also see very very carefully, I am using "x" for cone height. h is for slant height here. (I'm using slightly different variables for surface area than for volume).