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2007
Mon
10
Sep
Miss Loi avatar

Which Ice Cream Cone Should She Choose?

(11)
Tuition given in the topic of E-Maths Tuition Questions from the desk of Miss Loi at 12:42 pm (Singapore time)

Yay! The September term break is finally over! It’s been an epic week of intensely choking joss sticks smoke, intensely havoc students, and … umm … intense gastric pains 🙁

To ‘celebrate’ her temporary liberation from havoc students and gastric pains, Miss Loi decided to reward herself with some yummy ice-cream. And so fate has it that she approached an ice cream uncle in between some hardcore shopping at Orchard Road.

This ice cream uncle was unique. He actually sold them in cones of two sizes. Seeing that the size of the large cone could end up with her paying more for a visit to Mary Chia, Miss Loi decided to go for the small cone.

But here’s the twist: the uncle has two different types of small cones which he insisted are of the same size and volume. However, Miss Loi smelled a rat and a quick scan with her super-duper bionic eyes revealed the following:

It was indicated on the large cone (with base radius r mm and height h mm) that its volume is 320 mm3.

  1. Small cone A has a base radius of {3/4}r mm and height of {1/2}h mm.
  2. Small cone B is similar to the large cone, with a base radius of {3/4}r mm.

Fears of Mary Chia aside, she still doesn’t want to be ripped off by this ice cream uncle! So can you help Miss Loi decide which cone (A or B) to get?

IMPORTANT: Miss Loi left her calculator in the car! So please don’t waste time trying to calculate stuffs like h and r! Also she’s kicking herself for also leaving in the car her textbook with the Similarity and Congruency chapter, the chapter that contains some obscure formulae for non-triangular figures which her students always never memorize!

頑張って!!!

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Comments & Reactions

11 Comments

  1. eastcoastlife's Avatar
    eastcoastlife commented in tuition class


    2007
    Sep
    11
    Tue
    1:33pm
     
    1

    OMG! Buy one ice-cream cone also need to do Maths sum. I give up. I go Swensen's eat Earthquake.

  2. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    12
    Wed
    12:36am
     
    2

    Hehe guess this is 职业病…. What to do?

  3. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    12
    Wed
    6:19pm
     
    3

    CONE A CONE A!~(tho i feel b is larger in substance but de bigger it is de bigger de toothache is too>.>)

    for the largecone {1/3} * pi * r^2 * h =320

    πr2h = 960 (volume is fixed as per se)

    volume for cone A: {1/3} * ({3/4} r)^2 * {h/2} Don't miss out the π in your working!
    volume ={1/3} * (9/16)r^2 * {h/2} x π
    volume = {9/96} * pi * r^2 * h = {9/96} * 960 ( ∵ πr2h = 960)
    volume = 90 for cone a..90mm3?

    cone B on de otherhand..let r of cone b be k
    and volume of cone b be L

    k/r = 3/4 (given)

    (3/4)^2 = L/320

    L = 180 (An incredulous 90mm discrapancy..time to call CASE and start sueing?)

  4. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    12
    Wed
    11:49pm
     
    4

    Kiroii, cheers to you for getting the volume of Cone A correctly (As usual, please see comments in red).

    For Cone B, before you start calling CASE, please quickly open your textbook and refer to the formula for similar figures. Look under the one that deals with the volumes of two similar figures.

  5. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    13
    Thu
    1:05pm
     
    5

    huh?>.< i dun get what u mean by opening my text book and refering to the formula for similar figures..got formula *meh? if memory serves it's jus ratio?

  6. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    13
    Thu
    1:05pm
     
    6

    OH NOW I SEE LOL! i shouldnt have square it should have cubed it LOL! kk got iit got it..sry sry carelessness

  7. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    13
    Thu
    9:58pm
     
    7

    Yes it is vital to remember that for two similar figures X and Y,

    For volume, you cube the dimensional ratio: V_x/V_y = (r_x/r_y)^3

    For area, you square the dimensional ratio: A_x/A_y = (r_x/r_y)^2

    So can you find the volume of Cone B now?

  8. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    13
    Thu
    10:13pm
     
    8

    and volume of cone b be L

    k/r = 3/4 (given)

    (3/4)^3 = L/320

    L =136 135 (never-de-less still having disparity furthermore his context of admission that both cones are equal should be more then enough to call CASE against unscrupulous businessmen..)

  9. Miss Loi's Avatar
    Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class


    2007
    Sep
    13
    Thu
    11:05pm
     
    9

    Umm ... please see correction. Your working's fine but you really need to cut down on your careless mistakes.

    Anyway consumer rights are an urban legend in Singapore 🙂

  10. kiroii's Avatar
    kiroii commented in tuition class


    2007
    Sep
    15
    Sat
    3:22pm
     
    10

    true cant refute that..one can hardly assert himself

  11. Anoneemers's Avatar
    Anoneemers commented in tuition class


    2008
    Oct
    25
    Sat
    5:58pm
     
    11

    Actually its quite easy to determine which cone is bigger...they have the same radius (3/4r)mm but cone A has height of (1/2h)mm while cone B has height of (3/4h)mm-since B similar to larger cone
    since (3/4) > (1/2), B is larger than A.

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