2007
Mon
10
Sep

# Which Ice Cream Cone Should She Choose?

(11)
Posted at 12:42 pm

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 mm and height of mm.
2. Small cone B is similar to the large cone, with a base radius of 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!

### Revision Exercise

To show that you have understood what Miss Loi just taught you, you must:

1. 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. 2007
Sep
12
Wed
12:36am

2

Hehe guess this is 职业病…. What to do?

3. kiroii says

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

πr2h = 960 (volume is fixed as per se)

volume for cone A: Don't miss out the π in your working!
volume = x π
volume = ( ∵ 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. 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 says

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 says

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. 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:

For area, you square the dimensional ratio:

So can you find the volume of Cone B now?

8. kiroii says

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. 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 says

2007
Sep
15
Sat
3:22pm

10

true cant refute that..one can hardly assert himself

11. Anoneemers says

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.

• ### Latest News

The completion of the Second Temple is nigh!

Just in time for the June Holiday Intensive Jφss Sticks tuition sessions to save EMaths, AMaths, Chemistry, Physics & Social Studies students who may be still reeling from their "满江红" mid-year exam results :\

Contact Miss Loi to confirm your salvation and rid yourself of the LMBFH Syndrome from the subject(s) of your choice this June holiday!

Subscribe to Miss Loi's 2012 Maths Exam Papers now, with a subscription period that lasts right up till 31 Dec 2013!

Suggested solutions & answers to selected Oct/Nov 2012 GCE 'A'/'O' Level Maths (EMaths, AMaths, H1, H2 Maths & Science (Physics, Chemistry, Combined Science) papers are out!

Check out them out here »

* Please refer to the relevant Ten-Year Series for the questions of these suggested solutions.

• ### Study Room Access

• WP Cumulus Flash tag cloud by Roy Tanck and Luke Morton requires Flash Player 9 or better.

More Mathematical Topics →

• ### Greatest Chatterboxes

(of the Month)

1. None yet!

Subscribe to:

Miss Loi is a full-time private tutor in Singapore specializing in O-Level Maths tuition. Her life's calling is to eradicate the terrifying LMBFH Syndrome off the face of this planet. For over 22 years she has been a savior to countless students ... [read more]

• ### Gratitudes

I was confident for the 'O' Levels as I knew that Miss Loi had prepared me very well. I ended up achieving A1 for both EMath and AMath ... [read more]

Brenda Kong
Singapore Chinese Girls' School