Conor wants to put a moat around his rectangular castle. Let m = the width of the moat. The castle is 60 ft long and 45 ft wide. The moat is 10 ft wide and 10 ft deep. Calculate how many gallons of...

Conor wants to put a moat around his rectangular castle. Let m = the width of the moat.

The castle is 60 ft long and 45 ft wide. The moat is 10 ft wide and 10 ft deep.

Calculate how many gallons of water are in the moat if 1 gallon = 0.134 ft^3. Round your answer to the gallon.

Asked on by loishy

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tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

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We need to find the volume of a 10 foot wide, 10 foot deep moat around a castle with dimensions of 45 ft x 60 ft.  If I draw a diagram of the moat around the castle:  I break the moat into a series of rectangles and squares.  2 rectangles measuring 60m, 2 measuring 45m and 4 squares `` .  The question tells us that m stands for the width of the moat and that the moat is 10 feet wide, that means `` plugging that value into our original formulas we get that the moat covers an area of `` We also know that V=Base x Height.  We already know the base is 2500 sq. ft.  We also are told that the moat is 10 ft deep (height).  Plug that into the equation and we find the volume of the moat ``

Now we need to convert that into gallons.  We've been given a conversion factor of 1 gal = 0.134 cu. ft.  We need to know how many 0.134 cubic foot increments are in 25,000 cubic feet.  We do this by dividing `25,000-:0.134~~186,567` So we find that the moat contains 186,567 gallons of water, to the nearest gallon. 

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