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3 years ago

6

Use Cavalieri’s Principle to calculate the exact volume of an oblique cylinder with a height of 10 meters and a circular base wi

th a radius of 8 meters

2 answers:

nirvana33 [79]3 years ago

7 0

Answer: Volume of an oblique cylinder is 2011.43 sq.m.

Step-by-step explanation:

Since we have given that

Radius of a cylinder = 8 meters

Height of a cylinder = 10 meters

Cavelieri's Principle states that volume of an oblique cylinder is same as the volume of right circular cylinder with equal radius and height.

As we know the formula for "Volume of cylinder":

$Volume=\pi r^2h\\\\V=\frac{22}{7}\times 8\times 8\times10\\\\V=\frac{14080}{7}\\\\V=2011.43$

Hence, Volume of an oblique cylinder is 2011.43 sq.m.

Aleksandr-060686 [28]3 years ago

4 0

I think it is 640 pi

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Divide using long division.

elena55 [62]

You will get
3d-7- 8/d+3

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2 years ago

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Olin [163]

So here, ABCD is being inscribed in a circle, so ABCD is a cyclic quadrilateral (as inscribed in a circle) also, there exists a property of cyclic quadrilateral, i.e, the sum of opposite angles of a cyclic quadrilateral is 180°, so we can just write the following equation using this :

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2 years ago

What is the area,in square centimeters,of a circle that has a circumference of 16 centimeters?

Ray Of Light [21]

Answer: $20.38\ cm^2$

Step-by-step explanation:

We know that the circumference of a circle is given by :-

$C=2\pi r$ , where r is the radius of the circle .

Given : Circumference of circle = 16 cm

Then, $16=2\pi r$

i.e $r=\dfrac{16}{2\pi}=\dfrac{8}{\pi}$ (1)

We know that the area of circle is given by :-

$A=\pi r^2$

i.e. $A=\pi (\dfrac{8}{\pi})^2$ [From (1)]

i.e. $A=\pi (\dfrac{64}{\pi^2})$

i.e. $A=\dfrac{64}{\pi}$

Put $\pi=3.14$

$A=\dfrac{64}{3.14}=20.3821656051approx20.38\ cm^2$

Hence, area of circle = $20.38\ cm^2$

5 0

2 years ago

Find a polynomial f(x) of degree 3 with real coefficents and following zeros. -4,4i

ElenaW [278]

Answer:

$f(x)=x^3 +4x^2 +16x +64$

Step by step explanation:

$\text{Given that, two roots are}~ -4~ \text{and}~ 4i.\\\\\text{Let,}\\\\~~~~~~~x = 4i\\\\\implies x^2 = 16i^2~~~~~~~;[\text{Square on both sides}]\\\\\implies x^2 = -16~~~~~~~~;[i^2 = -1]\\\\\implies x^2 +16 = 0\\\\\text{So,}~ x^2 +16~ \text{ is a factor of the 3 degree polynomial}.\\ \\ \text{The polynomial is ,}\\\\ f(x) = (x+4)(x^2 +16)\\\\~~~~~~~=x^3 +16x +4x^2 +64\\\\~~~~~~~=x^3 +4x^2 +16x +64$

7 0

2 years ago

A wooden artifact from an ancient tomb contains 20 percent of the carbon-14 that is present in living trees. How long ago, to th

maxonik [38]

Answer:

The artifact was made approximately 13,306 years ago

Step-by-step explanation:

The half-life of Carbon-14 = 5730 years

The formula for radioactive decay is given by the equation:

$N=N_0 e^{- \lambda t}\\where:\\N = Number\ of\ particles\ at\ time\ t\\N_0= Number\ of\ particles\ at\ time\ t_0\\\lambda = decay\ constant = \frac{In}{t_{1/2}} ; t_{1/2} = half-life\\t = time\ in\ years$

The amount of Carbon-14 left = 20% = 20/100 = 0.2

$\therefore \frac{N}{N_0} = 20 \% = 0.2$

$N=N_0 e^{- \lambda t}\\\\dividing\ both\ sides\ by\ N_0\\\frac{N}{N_0} = e^{- \lambda t}\\0.2 = e^{- \lambda t}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.2 = Ine^{- \lambda t}\\In0.2 = -\lambda \times t\\but\ \lambda = \frac{In2}{t_{1/2}} \\\therefore In0.2 = -\lambda \times t\\\\= In0.2 = - \frac{In2}{t_{1/2}} \times t\\where\ t_{1/2} = 5730\ years\\-1.6094 = - \frac{0.6931}{5730} \times t\\-1.6094 = - 0.00012095 \times t\\t = \frac{-1.6094}{-0.00012095} \\t = 13,306.32$

t ≈ 13,306 years

7 0

2 years ago