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Three tennis balls

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Three tennis balls [#permalink] New post 25 May 2018, 16:24
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Question Stats:

93% (01:00) correct 6% (00:24) wrong based on 15 sessions
Attachment:
tennis.jpg
tennis.jpg [ 3.51 KiB | Viewed 429 times ]


Three tennis balls of identical size are stacked one on top of the other so that they fit exactly inside a closed right cylindrical can, as shown.

Quantity A
Quantity B
The height of the stack of 3 balls
The circumference of one of the balls
[Reveal] Spoiler: OA

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Re: Three tennis balls [#permalink] New post 29 May 2018, 06:37
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Carcass wrote:
Attachment:
tennis.jpg


Three tennis balls of identical size are stacked one on top of the other so that they fit exactly inside a closed right cylindrical can, as shown.

Quantity A
Quantity B
The height of the stack of 3 balls
The circumference of one of the balls


Let's examine Quantity A first

Let r = the radius of a tennis ball
Image


This means the HEIGHT of one tennis ball = r + r = 2r
Image
So, the height of the can = r + r + r + r + r + r = 6r

So, Quantity A = 6r

-----------------------------------
Now let's deal with Quantity B
Image

The circumference of a ball with radius r = the circumference of a circle with radius r
The circumference of a circle = 2πr
So, Quantity B = 2πr

-----------------------------------
We have:
Quantity A: 6r
Quantity B: 2πr

Since π ≈ 3.14, we know that 2π ≈ 6.28

So, we have:
Quantity A: 6r
Quantity B: 6.28r

We can see that Quantity B is greater.

Answer: B

Cheers,
Brent
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Re: Three tennis balls [#permalink] New post 29 May 2018, 10:50
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GREAT explanation Sir.

Regards
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Re: Three tennis balls [#permalink] New post 29 May 2018, 18:05
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Carcass wrote:
GREAT explanation Sir.

Regards


Thanks!!!
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Re: Three tennis balls [#permalink] New post 06 Jul 2018, 06:12
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Carcass wrote:
Attachment:
tennis.jpg


Three tennis balls of identical size are stacked one on top of the other so that they fit exactly inside a closed right cylindrical can, as shown.

Quantity A
Quantity B
The height of the stack of 3 balls
The circumference of one of the balls



Here,

Lets take diameter of the 1 tennis ball = 10 cm

so radius of the 1 tennis ball = 5 cm

Now QTY A;

Height of 3 tennis ball = 10 + 10 + 10 = 30 cm (i.e. the sum of the diameter of the tennis ball will give the total height)


Now QTY B

Circumference of 1 tennis ball = 2 * \pi * Radius = 2 * 3.14 * 5 = 31.4

Hence QTY A > QTY B.

**The diameter can be any value, for easy calculation 10 is assumed.
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Re: Three tennis balls   [#permalink] 06 Jul 2018, 06:12
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Three tennis balls

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