



 
Hi Jason, The shape you have is called a truncated cone and you can see the volume as the difference between the volumes of two cones. The volume of a cone is 1/3 π r^{2} h where r is the radius of the base, h is the height and π is approximately 3.1416. For your two cones the radius of the base of the larger cone is BC = 36 inches and the radius of the base of the larger cone is DE = 25/2 inches. The heights are h + 48 inches and h inches. Thus if you can find the length AD = h you can calculate the volumes. The key to finding h is the triangles ADE and ABC. These triangles are similar so
Solving for h gives h = (48 × 25)/47 = 25.53 inches. Use the expression for the volume of a cone to calculate the volumes of the two cones and then subtract these values to find the volume of the truncated cone. I hope this helps,  


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