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    Struggling to understand it

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    i will give you hints for a) and b)..

    When you think of scale factor, think of the ratios of corresponding "measuements" of "similar" objects, like sides or height.

    a) The key words in the question are: "...what is the scale factor of the lengths of the large cone to the small cone"

    i.e. what is the ratio of any available measurement of length in the large cone to a corresponding one in the small cone?

    What about the height? - the question tells us that the large cone is 15cm in height, and the frustrum is 10 - leaving 5, so scale factor of "large to small"

    is\displaystyle \frac{L_{h}}{S_{h}} i.e. large height to small height ("small to large scale factor is just the reciprocal of this)

    for b) if the scale factor of length is "m" , say, the scale factor of surface area will be m^{2}

    i.e. the large cone`s surface area will be m^{2} times bigger than the smaller one`s, and the small one`s is already given - (careful! - need to clarify if this is entire or lateral surface area)

    The (entire, including base) surface area of a cone is \pi r(\sqrt{r^{2}+h^{2}})+r) (just the 1st bit multiplied out if lateral area)

    Lateral surface area is: \pi r \sqrt{r^{2}+h^{2}})

    To get the surface area of the large cone, multiply the surface area of the small one by the area scale factor...

    m^{2} which you obtained from the above ratio...

    (As a check, put both in the ratio of "large cone area to small cone area, and you should get the correct factor - hint: 9)

    (EDITED)
 
 
 
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