Find surface area to volume ratio

**xxivythistlexx** · October 17th 2010, 08:03 AM

SHOW WORK PLEASE!
1st find SA, then volume, then the ratio

1. 2cm x 3cm x 4cm
2. 6 cm x 8 cmx 10cm
3. Radius = 4 cm
4 Radius = .75

**Unknown008** · October 17th 2010, 08:14 AM

Are those cuboids?

If so,

$Volume_{cuboid} = l\times b \times h$

$Volume_{sphere} = \dfrac43 \pi r^3$

$SA_{cuboid} = 2 lb + 2 lh + 2 lh$

$SA_{sphere} = 4\pi r^2$

Ratio will be simple then.

**xxivythistlexx** · October 17th 2010, 08:28 AM

I know the formulas, it just doesn't work when I do it or is a decimal.

**Unknown008** · October 17th 2010, 08:33 AM

Why not?

a) $Volume = lbh = (2)(3)(4) = 24 cm^3$

$SA = 2(2)(3) + 2(3)(4) + 2(2)(4) = 12 + 24 + 16 = 52 cm^2$

Ratio = 24 : 52 = 6 : 13

**xxivythistlexx** · October 17th 2010, 08:51 AM

Thanks, I already got that one. It's just the last two with decimals that I can't solve.

**Unknown008** · October 17th 2010, 09:01 AM

$Volume = \dfrac43 \pi (4)^3 = \dfrac43 \pi (64) = \dfrac{256\pi}{3} cm^3$

$SA = 4 \pi (4)^2 = 64 \pi\ cm^2$

Ratio = 256/3 : 64 = 4 : 3

**xxivythistlexx** · October 17th 2010, 09:24 AM

Thank you, thank you, thank you!
But I'm still getting a decimal on the last one D:

**Unknown008** · October 17th 2010, 09:48 AM

Really? =/

$Volume = \dfrac43 \pi (0.75)^3 = \dfrac{9\pi}{16}$ cm^3

$SA = 4\pi (0.75)^2 = \dfrac{9\pi}{4}$ cm^2

Ratio = 9/16 : 9/4 = 4 : 16 = 1 : 4

**xxivythistlexx** · October 17th 2010, 09:56 AM

Yeah, I know, but I missed class on Thursday/Friday so I wasn't exactly taught how to do it.
Also, for #2, the ratio 188:225 isn't right, is it?

**Unknown008** · October 17th 2010, 10:00 AM

Oo

$Volume = (8)(6)(10) = 480$ cm^3

$SA = 2(8)(6) + 2(8)(10) + 2(6)(10) = 376$ cm^2

Ratio = 480: 376 = 60 : 47

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