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
Mar 29, 2018
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"#