Q:

Answer:Part A) The volume of the entire cone is $$168\pi\ in^3$$Part B) see the explanationStep-by-step explanation:Part A) we know thatThe volume of a cone is equal to$$V=\frac{1}{3}\pi r^{2}h$$wherer is the radius of the base of the coneh is the height of the coneIn this problem triangle ABD is similar to triangle ACERemember that If two figures are similar, then the ratio of its corresponding sides is proportionalso$$\frac{AB}{AC}=\frac{BD}{CE}$$substitute the given values$$\frac{7}{14}=\frac{3}{x}$$solve for x$$x=14(3)/7\\x=6\ in$$To find out the volume of the entire cone we have$$r=CE=x=6\ in$$$$h=AC=14\ in$$substitute in the formula$$V=\frac{1}{3}\pi (6)^{2}(14)$$$$V=168\pi\ in^3$$Part B) How did you determine the value for x in triangle ACEIn this problem triangle ABD is similar to triangle ACEIf two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruentso$$\frac{AB}{AC}=\frac{BD}{CE}$$substitute the given values and solve for x