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2 years ago

Help ASAP!!

2 answers:

5 0

Circumference of a circle - derivation

This page describes how to derive the formula for the circumference of a circle.

Recall that the definition of pi (π) is the circumference c of any circle divided by its diameter d. Put as an equation, pi is defined as

π

=

c

d

Rearranging this to solve for c we get

c

=

π

d

The diameter of a circle is twice its radius, so substituting 2r for d

c

=

2

π

r

If you know the area

Recall that the area of a circle is given by

area

=

π

r

2

Solving this for r

r

2

=

a

π

So

r

=

√

a

π

The circumference c of a circle is

c

=

2

π

r

DENIUS [597]2 years ago

4 0

Answer:

4.) Find the length of the diameter and the length of the circumference of the circle. Divide the length of the circumference by the length of the diameter. Set up an equation showing the ratio of the circumference to the diameter equal to π . Then rearrange the equation by solving it for the circumference. Substitute 2 times the radius for the diameter.

Step-by-step explanation:

I know I just took the quiz

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Answer:

$b=h=\sqrt{6}$ m

Step-by-step explanation:

Let

Bas length of box=b

Height of box=h

Material used in constructing of box=36 square m

We have to find the height h and base length b of the box to maximize the volume of box.

Surface area of box= $2b^2+4bh$

$2b^2+4bh=36$

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$2bh=18-b^2$

$h=\frac{18-b^2}{2b}$

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Substitute the values

$V=b^2\times \frac{18-b^2}{2b}$

$V=\frac{1}{2}(18b-b^3)$

Differentiate w. r.t b

$\frac{dV}{db}=\frac{1}{2}(18-3b^2)$

$\frac{dV}{db}=0$

$\frac{1}{2}(18-3b^2)=0$

$\implies 18-3b^2=0$

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$b=\sqrt{6}$

The negative value of b is not possible because length cannot be negative.

Again differentiate w.r.t b

$\frac{d^2V}{db^2}=-3b$

At $b=\sqrt{6}$

$\frac{d^2V}{db^2}=-3\sqrt{6}$

Hence, the volume of box is maximum at $b=\sqrt{6}$ .

$h=\frac{18-(\sqrt{6})^2}{2\sqrt{6}}$

$h=\frac{18-6}{2\sqrt{6}}$

$h=\frac{12}{2\sqrt{6}}$

$h=\sqrt{6}$

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