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  Games R' Us Giraffes - $7 Mathematics Quiz

  Games R' Us Giraffes - $7 Mathematics Quiz
   
  
  David’s project deadline was approaching soon. That day, he was still sitting at his desk after office hours and was still thinking the best way to finish his project on time. He was exited after...

  • July 31, 2021

  • Zarin sadaf snigdha likes this.
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    Zarin sadaf snigdha Since both the Giraffes are similar & we know the volume & heigh of larger Giraffe & the height of the smaller Giraffe we can use Similarity to find the volume of smaller Giraffe.
    (Volume of smaller/ volume of larger) = (height of smaller/...  moreSince both the Giraffes are similar & we know the volume & heigh of larger Giraffe & the height of the smaller Giraffe we can use Similarity to find the volume of smaller Giraffe.
    (Volume of smaller/ volume of larger) = (height of smaller/ height of larger)^3
    (X/5400) = (4/6)^3
    X= 1600m3
    So the volume of smaller Giraffe is 1600 m3
    This method will give us a very accurate volume of the smaller Giraffe as the Giraffes are similar means that the smaller one is a scaled down version of the larger one so dimensions are proportional to the volume. We cubed the length so that we can take it to meter cube & get the volume.  less

    • July 30, 2021
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    Shadman Chowdhury The volume of the smaller giraffe will be found by different methods. If the first approach doesn't work, try another method.
    
    The formula for calculating volume is: V=L*W*H where L is length, W is width and H is height. As you can see in the diagram...  moreThe volume of the smaller giraffe will be found by different methods. If the first approach doesn't work, try another method.
    
    The formula for calculating volume is: V=L*W*H where L is length, W is width and H is height. As you can see in the diagram above, the L of the smaller giraffe is 6m and its width and height are both 1m each. Thus the total surface area (6x1) + (1x1)=7 sq m.
    
    Since we know that the larger giraffe has a volume of 5400 m³, we need to find how many times more or less than this number 7sq m represents when compared to the larger giraffe with a volume of 5400 m³.
    
    Continue to the second comment...  less

    • July 31, 2021
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    Shadman Chowdhury The first method is to calculate the ratio of the surface area of a smaller giraffe compared to that of the larger one and then multiply this number with the volume of a larger giraffe. This will give us an approximate answer for the volume of the...  moreThe first method is to calculate the ratio of the surface area of a smaller giraffe compared to that of the larger one and then multiply this number with the volume of a larger giraffe. This will give us an approximate answer for the volume of the smaller giraffes.
    
    Using generic maths formula, we can write: Given: L=6, W = 1 & H=1 --> So, S=(6x1)+(1x1)=7 sq m --> VL=5400 (given) --> RATIO=(Total Surface Area)/ Volume --> S/VL = 7/(5400) or 0.0118696... (approx.)
    
    Thus, we have a ratio of 0.0118696... (approx.) between the surface area of the smaller giraffe and a larger one. Now we need to multiply this number with the volume of the larger giraffe in order to find out how many times the smaller giraffe's volume is compared to that of the larger giraffe.
    
    This gives us a more accurate answer for the volume of smaller giraffes! Vsmaller Giraffes =0.0345691...(approx.) or 836 m³  less

    • July 31, 2021
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    Zakaria Ahomed First of all the main thing comes here is about similarity. But a difference in case of height and dimensions. So in this case we can do following things.
    Suppose,the volume of smaller one = x
    Ratio of their Heights => 4/6= 2/3
    Again,if we cube...  moreFirst of all the main thing comes here is about similarity. But a difference in case of height and dimensions. So in this case we can do following things.
    Suppose,the volume of smaller one = x
    Ratio of their Heights => 4/6= 2/3
    Again,if we cube this the result will be(2/3)^3= 8/27.
    This is similar as the volume so we can write a equation with it. Now, the equation stands → 8/27=x/5400
    x=1600m3
    Smaller giraffe's volume is 1600m3
    Now, 'How my formula will work?' that's the question. The very first thing mentioned here is they are similar. That means ratio of length, width and height will be same. We were given with two heights. From that we have calculated the ratio. And the least form came 2/3 that means it can't be divided any further. So,it is the common ratio among the length,width and height.
    But this ratio isn't equal to ratio of volume.For making this equal to volume. We need to cube it. Why? That's because If two solids are similar, the ratio of their volumes is equal to the cube of...    less

    • July 31, 2021
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    Zakaria Ahomed That's because If two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides.The cube came 8/27. And the rest of the things are as given. The equation will be (common ratio)^3=ratio of volumes. Thus...  moreThat's because If two solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding sides.The cube came 8/27. And the rest of the things are as given. The equation will be (common ratio)^3=ratio of volumes. Thus it will work.
    Now, the question remains, 'why it will work?' It will work because,I have done the correct things. Now, imagine one thing. I could show ratio of sides equal to the ratio of volumes. In that case that won't be correct and the answer would be 3600m3. Because,a one dimensional unit can't be equal to a three dimensional unit.  less

    • July 31, 2021
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    • 1 likes this
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    Tanveer Tausif Ratul Height of bigger giraffe, Hbig=6m
    Height of smaller giraffe, Hsmall=4m
    Volume of bigger giraffe, Vbig=5400m3
    Volume of smaller giraffe, Vsmall=X...  moreHeight of bigger giraffe, Hbig=6m
    Height of smaller giraffe, Hsmall=4m
    Volume of bigger giraffe, Vbig=5400m3
    Volume of smaller giraffe, Vsmall=X (let)
    
    
    If we use similarity formula,then,
    Hbig/Hsmall=Vbig/Vsmall
    
    
    But in an equation,the dimensions of the both sides must beequal.In this equation,height is a one-dimensional unit (m),but volume is a three-dimensional unit (m^3).In order to satisfy the condition of an equation,we have
    to take the cube of both "Hbig" & "Hsmall".Then the
    values will be 216 & 64 accordingly.Now the dimension has become equal & the equation is absolutely correct.
    
    
    So,putting these values,the equation will be- 216/64=5400/X
    
    
    From the equation,value of X is 1600
    So, the volume of smaller giraffe is, Vsmall=1600m3  less

    • July 31, 2021
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    Kanta Akter We can just simply do this calculation as the Giraffes are similar. the bigger one is 4/6 times the smaller one in all three dimensions that result in a smaller one 5400×4/6×4/6×4/6 or 5400×(4³/6³)=1600m³
    
    Then why this will...  moreWe can just simply do this calculation as the Giraffes are similar. the bigger one is 4/6 times the smaller one in all three dimensions that result in a smaller one 5400×4/6×4/6×4/6 or 5400×(4³/6³)=1600m³
    
    Then why this will work?
    
    If two giraffes are similar then their corresponding linear measures (widths, heights, base lengths, etc.) are proportional too. And we also know volume is expressed in the cubic unit because it is the sum of three measurements (length, width, and depth) that are multiplied together. Cubic units are cm3, m3 , and cubic feet.
    
    Now, the main point is which toy size he should keep for manufacturing more toys?
    
    I think he should manufacture smaller giraffes since small things are sturdier in proportion to their size. Moreover, the small Giraffe will be able to hold up fine. But, the larger giraffe built with the same proportions as the small one will collapse under its weight. This large giraffe also needs to have timbers that are thicker compared to its size. That's...    less

    • July 31, 2021
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    Kanta Akter That's why a small giraffe will be the best choice for manufacturing.

    • July 31, 2021
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    Nirjona Akter In the passage, it is stated that giraffes are similar with different sizes. We can calculate the volume of a smaller giraffe by using given values along with simple math calculation. So If the height of 6 makes a 5400 m³, then the first part of the...  moreIn the passage, it is stated that giraffes are similar with different sizes. We can calculate the volume of a smaller giraffe by using given values along with simple math calculation. So If the height of 6 makes a 5400 m³, then the first part of the proportion is 6/5400 m³ The second part of the proportion has a numerator of 4 because of the height of 6 changes into a height of 4. The proportion should be set up as 6/5400m³=4/x because the bottom number is the volume, and the top is the height, and we want to find the volume of the similar smaller giraffe.
    
    To solve the proportion, let's suppose smaller giraffe volume is x, so if we cross multiply the numerator and denominator, so it would be in this way,
    
    6x=5400m³*4
    
    or,x/5400 m³=4/6
    
    or,x/5400m= (4/6)³
    
    or,x=(5400×64)/216
    
    x=1600  less

    • July 31, 2021
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    Nirjona Akter Why this formula will work?
    
    This method will work when all the sides are of the same length. Then, we can find the volume of a cube just knowing the measurement of only one side. If a cube has side length "x" then Volume = x × x × x a which results in...  moreWhy this formula will work?
    
    This method will work when all the sides are of the same length. Then, we can find the volume of a cube just knowing the measurement of only one side. If a cube has side length "x" then Volume = x × x × x a which results in the formula, Volume = x³. This is where we get the term called"cubed". When we use power to the 3 over something, we call it cubed. When units of Measure are calculated, we find the volume of an object, and the units are cubed. This means that if the measurements of the sides are in miters, then the answer will be in cubed miters.  less

    • July 31, 2021
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    Shaikh Nafisa Binte Fahad ''How will it work?''
    In question, it represents the subject of ‘similarity statistics’. This means that the ratio of height, length, and width will be the same.
    In the equation, we are seeing that the dimension of both the values are different which...  more''How will it work?''
    In question, it represents the subject of ‘similarity statistics’. This means that the ratio of height, length, and width will be the same.
    In the equation, we are seeing that the dimension of both the values are different which needs to be equal. Over here, the height is a one-dimensional unit(meter) but the volume is three-dimensional (meter^3). So, we need to cube it to make it evenly dimensional.
    ''Why would it work?''
    Otherwise, it is not according to the rules and the answer will be wrong.
    So, given,
    Height of small giraff= 4m
    = 4 x 4 x4 = 216m^3
    Height of big giraff= 6m
    = 6x 6 x6 = 64 m^3
    Volume of big giraff= 5400m^3
    and, let the volume of small giraffe be 'x' m^3.
    Now. we know,
    the formula of similarity,
    Height of big giraffe/Height of small giraffe=Volume of big giraffe/Volume of small giraff.
    ==> 216/64 = 5400/ 'x'
    ==>216x =345600
    ==> x =1600
    Therefore, the volume of the small giraff is 1600 m^3.  less

    • July 31, 2021
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    • 1 likes this
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    Noorjahan Binte Farhana There is given Small and tall giraffe height. And the tall giraffe volume is 5400 meter queb. volume= length × width × height.
    consume the length X and width Y for tall and small giraffe
    so, for tall giraffe...  moreThere is given Small and tall giraffe height. And the tall giraffe volume is 5400 meter queb. volume= length × width × height.
    consume the length X and width Y for tall and small giraffe
    so, for tall giraffe X*Y*6=5400
    XY=5400/6
    XY= 900
    Now, for small giraffe volume X*Y*4
    900*4=3600 [ we have find out XY=900]
    The tall giraffe is 1.5 tall more than small giraffe.
    as, 3600*1.5=5400  

    • August 1, 2021
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    Jesmin Akhter given,
    Bigger giraff height = 6m
    And the volume of bigger giraff = 5400m^3
    we know a formula...  moregiven,
    Bigger giraff height = 6m
    And the volume of bigger giraff = 5400m^3
    we know a formula that,
    volume = lenght * wide * hight
    let, lenght = a, wide = b
    so, volume = lenght * wide * hight
    => 5400m^3 = a * b * 6m
    => ab = 5400m^3 / 6m
    => ab = 900m^2 ...........(i)
    given, Smaller giraff hight = 4m
    know we have to be findout the volume of smaller giraff.
    let, volume of smaller giraff = x
    leangth = a
    wide = b
    we know,
    valume = length * wide * hight
    => x = ab * 4m
    => x = 900m^2 * 4m [ puting the value of a and b from equation...    less

    • August 1, 2021
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    Nur E ferdus Monika matin At first, it is mentioned that both giraffes are similar. That means the ratio of height, length,
    width, and the dimension of each part will be the same for the two Giraffe. The volume of a
    three dimensional figure is- volume= length X width X height so,...  moreAt first, it is mentioned that both giraffes are similar. That means the ratio of height, length,
    width, and the dimension of each part will be the same for the two Giraffe. The volume of a
    three dimensional figure is- volume= length X width X height so, Volume(Small)/Volume
    (Large)=Length(s)×width(s)×Height(s)/Length×width×Height
    Height(s)/Height=4/6=2/3 So, Length(s)/ Length=2/3 and width(s)/width=2/3
    Volume(Small)/Volume (Large)= (2/3) ×(2/3)×(2/3) Volume(Small)= (8/27)× Volume (Large)
    = (8/27) × 5400 m^3 = 1600 m^3 This formula will work because If we calculate volume part
    by part and make a sum to get the total volume of the small giraffe as it is irregular-shaped,
    it will remain unchanged because each part maintains the same ratio of 2/3 with the large
    Giraffe as both are similar.  less

    • August 1, 2021