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ACT Aspire Math: Defining the Relationship Between Radius and Area 0 Views
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Description:
The radii of two circles have a ratio of 1:4.
What is the ratio of their areas?
Transcript
- 00:01
Okay Math people The ray v i and yes that's
- 00:05
how you spell it Of two circles have a ratio
- 00:07
of one to four What is the ratio of their
- 00:10
areas Circle versus circle smackdown What we were all getting
- 00:20
to place a bet on which one of these circles
Full Transcript
- 00:23
would win a pie fight until we realized that this
- 00:26
problem doesn't even have any pie to settle the score
- 00:30
Well if two similar circles have radio in the ratio
- 00:32
of eight to be than their areas are in the
- 00:35
ratio of a swear to be squared and their volumes
- 00:38
Aaron the ratio a cube to be cubed But that's
- 00:41
a math factoid to save for a party that needs
- 00:43
livening up the areas of two circles in question have
- 00:46
a ratio of one squared to four squared which is
- 00:49
equivalent to a ratio of one to sixteen So if
- 00:53
you didn't remember this rule while you can also set
- 00:55
up a ratio using the area formula pi r squared
- 00:58
and you know your own numbers maintaining the ratio of
- 01:01
radio i wonder for a while we can imagine that
- 01:03
the first circle has a radius of two and the
- 01:05
second circle a radius of eight First circle would then
- 01:09
have an area of pi r squared or four pi
- 01:12
and the second circle would have an area of pie
- 01:14
eight squared or sixty four pi Well just cut out
- 01:17
the pie Serve yourself a slice and find the ratio
- 01:20
of four to sixty for which then simplifies to yes 00:01:23.812 --> [endTime] one to sixteen so the answer is d
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