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Hi guys we are working out the volume of a witch hat, have you ever seen him on the road
when your parents are driving along and there is a little witch hat stand out construction
site so that type of a thing well I find out an actual witch hat and I got the dimension
and I put them up here. What we are going to do?is we are going to work out complete
the entire volume in centimeters cube to the nearest centimeter cube of this particular
witch hat displayed in this diagram right over here. So we are going to take in two
phase, phase no. 1 is to work out he cone components see the cone on top we are going
to work out that, to get the volume of that then later we are going to work out the volume
of this rectangular prism setting underneath that cone together makes it a witch hat and
the answer will be to the nearest centimeter cube not to one decimal places, not to two
decimal places to the nearest centimeter cube. So let us start at phase no. 1 we are going
to work out volume for that cone so what do we need to do first? write up the formula
so the formula for the cone, if you recall is---
volume is 1/3 pi r squared x the h, so let us take a closer at this particular volume
all units are in centimeter and we have a height here of 62 cm that height is going
to go there, the radius over here to its left is 18cm right there from the center to the
edge so put the 18 there plug the rest in the formula and come up with the answer.
So let us do that now—let us put in the radius, the again radius is 18cm –and we
need to square that because that is what the formula says x the height and the height there
is 62 from the peak, the a peaks all the way there to the center of the base—ok let us
plunk that in our calculator, 1/3 x pi x 18 squared x 62, altogether to the nearest centimeter
cube –
ok that is the volume for the top part the cone component of this witch hat.
Let us go down below to the base; we have as I mentioned earlier a rectangular prism
and the dimension are all shown. So first things first we got to write go to the formula,
write up the formula for volume of a rectangular prism let us write that up now – and that is length x breath x height let us
have a look here. Length x breath x there is that little height there this is 5cm right
over there so its square base is 46cm by 46 therefore 46, let us plunk it into that formula.
So the length is 46 x 46 x the height which little 5cm right over there let us put our
5 there, x 5 ok let us plunk in our calculator. 46 x 46 x 5 altogether the entire volume for
that base for that rectangular prism down the bottom is ---
ok that is the bottom part there that is 10580 cm cube to the nearest centimeter cube. That
is rounded and this one here also rounded all we have to do is combine the 2 because
this is a composite shapes and we are looking for the volume together the complete total
entire volume of this witch hat is---let us add the two, this one + that one, and so 10580
+ 21036 altogether to the nearest centimeter cube give us the grand total of V total the
entire complete volume of this witch hat is ---
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