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alexandr402 [8]
3 years ago
10

Maekyala's Room is 65m by 3m by 3m.How many cubic meter of air will her room hold?

Mathematics
1 answer:
UNO [17]3 years ago
8 0

Answer:

<u>585 Cubic Meters</u>

Step-by-step explanation:

Since the room is in the shape of a rectangular prism, to find the volume, you'll do Volume = Length * Width * Height

So, 65 * 3 * 3 = 585 Cubic Meters

<em>(its in cubic meters because it is measuring a volume of space)</em>

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It sounds like <em>R</em> is the region (in polar coordinates)

<em>R</em> = {(<em>r</em>, <em>θ</em>) : 2 ≤ <em>r</em> ≤ 3 and 0 ≤ <em>θ</em> ≤ <em>π</em>/2}

Then the integral is

\displaystyle \iint_R\frac{\mathrm dx\,\mathrm dy}{\sqrt{x^2+y^2}} = \int_0^{\pi/2}\int_2^3 \frac{r\,\mathrm dr\,\mathrm d\theta}{\sqrt{r^2}} \\\\ = \int_0^{\pi/2}\int_2^3 \mathrm dr\,\mathrm d\theta \\\\ = \frac\pi2\int_2^3 \mathrm dr \\\\ = \frac\pi2r\bigg|_2^3 = \frac\pi2 (3-2) = \boxed{\frac\pi2}

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3 years ago
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