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zimovet [89]
2 years ago
10

Drag and drop an answer to each box to correctly complete the explanation for deriving the formula for the volume of a sphere.

Mathematics
2 answers:
Advocard [28]2 years ago
5 0
The volume of a sphere is given by:

V= \frac{4}{3} \pi r^{3}

So, we need to deduct this equation. We will walk through Calculus on the concept of a solid of revolution that is a solid figure that is obtained by rotating a plane curve around some straight line (the axis of revolution<span>) that lies on the same plane. We know from calculus that:

</span>V=\pi \int_{a}^{b}[f(x)]^{2}dx
<span>
Then, according to the concept of solid of revolution we are going to rotate a circumference shown in the figure, then:

</span>x^{2}+y^{2}=r^{2}
<span>
Isolationg y:

</span>y= \sqrt{r^{2}-x^{2}}<span>

So,

</span>f(x)=y=\sqrt{r^{2}-x^{2}}<span>

</span>V=\pi \int_{a}^{b}[\sqrt{r^{2}-x^{2}}]^{2}dx
<span>
</span>V=\pi \int_{a}^{b}(r^{2}-x^{2})dx<span>

being -r and r the limits of this integral. 

</span>V=\pi \int_{-r}^{r}(r^{2}-x^{2})dx
<span>
Solving:

</span>V=\pi[r^{2}x-\frac{x^{3}}{3}]\right|_{-r}^{r}

Finally:
<span>
</span>V=\pi(r^{3}-\frac{r^{3}}{3})-\pi(-r^{3}+\frac{r^{3}}{3})= \frac{4}{3} \pi r^{3}<span>
</span><span>
</span>

Vesna [10]2 years ago
5 0

Answer:

idk the answer but its not what that dude said

Step-by-step explanation:

hehe

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bogdanovich [222]

Answer:

D. About $10

Step-by-step explanation:

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For example - $56 divided by 6.2 pounds of pecans is 9.032258064516129032258064516129‬ which can be rounded up to about $10

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Step-by-step explanation:

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A car company sells a scale model to of the size of one of its cars.
mixer [17]

Answer:

w = 13500 --- real windscreen

v = 408 --- scale volume

Step-by-step explanation:

Given

k = \frac{1}{10} --- scale factor

See attachment

Required

Complete the table

To get the windscreen (w) of the real car, we do the following computation

w = \frac{w_{scale}}{k^2}

This gives:

w = \frac{135}{(1/10)^2}

w = \frac{135}{1/100}

w = 13500

Next, the volume (v) of the scale mode

We make use of the following computation

v = v_{real} * k^3

So, we have:

v = 408000 * (1/10)^3

v = 408000 * 1/1000

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Which function has the domain x&gt;or= -11
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y = \sqrt{x + 11}
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