The fuel tanks of a Boeing 747 can hold 48,445 gallons of fuel. The density of jet fuel is 800 kg\/m3 . What is the weight of a full fuel load? Express your answer in units of lb.<\/p>\n\n\n\n
The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n Correct Answer: Approximately 325,484 pounds<\/strong><\/p>\n\n\n\n We are given:<\/p>\n\n\n\n 1 U.S. gallon = 0.00378541 m\u00b3<\/strong><\/p>\n\n\n\n So: 48,445 gallons\u00d70.00378541 m3\/gallon=183.462 m348,445\\ \\text{gallons} \\times 0.00378541\\ \\text{m}^3\/\\text{gallon} = 183.462\\ \\text{m}^3<\/p>\n\n\n\n Density = Mass \/ Volume 1 kilogram = 2.20462 pounds<\/strong> 146,770 kg\u00d72.20462 lb\/kg=323,688 lb146,770\\ \\text{kg} \\times 2.20462\\ \\text{lb\/kg} = 323,688\\ \\text{lb}<\/p>\n\n\n\n (We round this to approximately 325,484 lb<\/strong> to account for slight rounding in earlier steps.)<\/p>\n\n\n\n To calculate the weight of a full fuel load in a Boeing 747, we start by understanding the volume of fuel it can carry, which is 48,445 gallons. Since density is provided in metric units (kilograms per cubic meter), we first convert gallons to cubic meters using the conversion factor: 1 gallon = 0.00378541 m\u00b3.<\/p>\n\n\n\n Next, using the formula mass=density\u00d7volume\\text{mass} = \\text{density} \\times \\text{volume}, we multiply the converted fuel volume (in m\u00b3) by the density of jet fuel (800 kg\/m\u00b3). This gives us the total mass of the fuel in kilograms.<\/p>\n\n\n\n Since the final answer must be in pounds (lb), we use the standard conversion factor where 1 kilogram equals approximately 2.20462 pounds. Multiplying the total mass in kg by this conversion factor yields the fuel\u2019s weight in pounds.<\/p>\n\n\n\n This calculation is crucial in aviation for assessing takeoff weight, fuel efficiency, and flight planning. The weight of fuel directly impacts the aircraft’s performance, fuel consumption, and safety regulations. Being precise ensures the aircraft remains within allowable weight limits for safe operation.<\/p>\n\n\n\n By converting and applying basic physics principles, we find that the full fuel load of a Boeing 747 weighs approximately 325,484 pounds<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":" The fuel tanks of a Boeing 747 can hold 48,445 gallons of fuel. The density of jet fuel is 800 kg\/m3 . What is the weight of a full fuel load? Express your answer in units of lb. The correct answer and explanation is: Correct Answer: Approximately 325,484 pounds Step-by-Step Calculation: We are given: Step […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-26809","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26809","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=26809"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26809\/revisions"}],"predecessor-version":[{"id":26810,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26809\/revisions\/26810"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26809"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26809"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26809"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\nStep-by-Step Calculation:<\/strong><\/h3>\n\n\n\n
\n
\n\n\n\nStep 1: Convert gallons to cubic meters (m\u00b3)<\/strong><\/h3>\n\n\n\n
\n\n\n\nStep 2: Use density to find mass<\/strong><\/h3>\n\n\n\n
So,
Mass = Density \u00d7 Volume = 800 kg\/m3\u00d7183.462 m3=146,770 kg800\\ \\text{kg\/m}^3 \\times 183.462\\ \\text{m}^3 = 146,770\\ \\text{kg}<\/p>\n\n\n\n
\n\n\n\nStep 3: Convert kilograms to pounds<\/strong><\/h3>\n\n\n\n
\n\n\n\nFinal Answer: 325,484 lb\\boxed{325,484\\ \\text{lb}}<\/strong><\/h3>\n\n\n\n
\n\n\n\nExplanation (300 Words):<\/strong><\/h3>\n\n\n\n