24 Jun ##V = 135 cm^3## Wow there is a lot of information given in
##V = 135 cm^3## Wow there is a lot of information given in these 2 sentences.! The first thing is to break down the information which is given into smaller parts. The phrase: the volume is given by means there is a formula and here it is So if you want to calculate the volume of the pyramid the formula you will have to use is: ##Vcolor(red)((x)) = 1/3(color(red)x^3+8color(red)x^2+16color(red)x) larr## the variables are all ##color(red)x## ##V(color(red)x)## means that the value of the Volume depends on the value of ##color(red)x## You are told ##color(red)x## is the height of the pyramid. So the height is needed for the formula. ##color(red)(x = height )## The base of the pyramid is a square You are also told that the height ##color(red)(x)## is based on the length of the side of the square. If you know the length of the side of the square you can work out the height. The height is 4 less than the length of the side ##rarr color(red)x = side -4## (So If the side is 12 then ##color(red)(x=8)## If the side is 25 then ##color(red)x=21## etc) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Now we are ready to find the answer! The side of the square is ##9 ## cm ##rarr color(red)(x= 9-4 =5cm) larr## (4 less) If ##color(red)(x=5)## you can find the volume by using ##color(red)(5) for color(red)x in V(color(red)x)## ##Vcolor(red)((x)) = 1/3(color(red)x^3+8color(red)x^2+16color(red)x)## ##Vcolor(red)((5)) = 1/3(color(red)5^3+8color(red)((5))^2+16color(red)((5))) larr## now calculate! ##V(5) = 1/3(125+200+80) = 1/3(405)## ##V = 135 cm^3##
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