Hi,
The cylinder's volume is pi*r^2*h. There are 3 ways to lay the crate: with the 8x10 side down, with the 8x12 side down or with the 10x12 side down.
Whether the 8x10 side or the 8x12 side is down, the maximum radius would be 4 feet (diameter 8 feet), so the 8x12 would give a larger height and larger volume..
With the 10x12 side down, the radius would have to be 5 (diameter 10).
Thus, the question is: would a cylinder with a radaius of 5 and a height of 8 have a greater volume or would the cylinder with a radius of 4 and a height of 12 have the greater volume. The pis cancel out, of course. 5^2*8 is 200. 4^2*12 is only 192.
Cheers,
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
