Acone-shaped dew collector has a height of 8 inches and holds 12 ounces of rain. What is the diameter of the collector in inches (use 1 ounce = 1.8 cubic inches)?

1 Answer
Jim G.
Mar 29, 2018

#"diameter "~~3.2" inches"#

Explanation:

#"using the following formulae"#

#•color(white)(x)V_(color(red)"cone")=1/3pir^2h#

#"where r is the radius and h the height"#

#•color(white)(x)"diameter (d)"=2r#

#"we are given that "V=12xx1.8=21.6" inches"^3#

#rArr1/3pir^2h=21.6larrcolor(blue)"multiply both sides by 3"#

#rArrpir^2h=64.8larrcolor(blue)"solve for r"#

#rArrr^2=64.8/(pih)=64.8/(8pi)#

#rArrr=sqrt((64.8)/(8pi))~~1.61" inches to 2 dec. places"#

#rArrd=2xx1.61~~3.2" inches"#

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