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EleoNora [17]
3 years ago
11

A trapezoid has 63.4 kilometers base and 23.2 kilometers base, as well as 75.3 kilometers height. What is the area?

Mathematics
2 answers:
andrew11 [14]3 years ago
8 0
A=(b1+b2) x height x 1/2
a=(63.4+23.2) x 75.3) x 1/2
a= 86.6x 75.3 x 1/2
a=6,520.98 x 1/2
a=3,260.49
Finger [1]3 years ago
7 0
Make sure to multiply everything together, then check it with a calculater.
Hope this works:)
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Answer:

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dm = ρ dV

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Substituting:

dm = ρ π r² dz

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dm = kz π r² dz

Next, we need to write the radius r in terms of the height z.  To do that, we need to look at the cross section (see image below).

The height z and the radius r form a right triangle, where the hypotenuse is the radius of the hemisphere R.

Using Pythagorean theorem:

z² + r² = R²

r² = R² − z²

Substituting:

dm = kπ z (R² − z²) dz

We now have the mass of each plate as a function of its height.  To find the total mass, we integrate between z=0 and z=R.

M = ∫ dm

M = ∫₀ᴿ  kπ z (R² − z²) dz

M = kπ ∫₀ᴿ (R² z − z³) dz

M = kπ (½ R² z² − ¼ z⁴) |₀ᴿ

M = kπ (½ R⁴ − ¼ R⁴)

M = ¼ k π R⁴

Next, to find the center of gravity, we use the weighted average:

zG = (∫ z dm) / (∫ dm)

zG = (∫ z dm) / M

We already found M, we just have to evaluate the other integral:

∫ z dm

∫₀ᴿ kπ z² (R² − z²) dz

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kπ (⅓ R² z³ − ⅕ z⁵) |₀ᴿ

kπ (⅓ R⁵ − ⅕ R⁵)

²/₁₅ k π R⁵

Plugging in:

zG = (²/₁₅ k π R⁵) / (¼ k π R⁴)

zG = ⁸/₁₅ R

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3 years ago
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