Ask question

Ask question

All categories

AlladinOne [14]

3 years ago

8

The surface area of a sphere is 576pi square units. Which choice represents the volume of the sphere?

1 answer:

Leona [35]3 years ago

3 0

Answer:

$\large\boxed{V=2304\pi}$

Step-by-step explanation:

The formula of a surface area of a sphere:

$S.A.=4\pi R^2$

R - radius

We have

$S.A.=576\pi$

Substitute and solve for R:

$4\pi R^2=576\pi$ <em>divide both sides by π</em>

$4R^2=576$ <em>divide both sides by 4</em>

$R^2=144\to R=\sqrt{144}\\\\R=12$

The formula of a volume of a sphere:

$V+\dfrac{4}{3}\pi R^3$

Substitute:

$V=\dfrac{4}{3}\pi(12^3)=\dfrac{4}{3}\pi(1728)=(4)\pi(576)=2304\pi$

You might be interested in

What is the equation of a circle whose radius is 16 units and center is at (2,-5)?

STatiana [176]

Answer:

The general equation of the circle is
$( {x - a})^{2} + ({y - b})^{2} = {r}^{2} \\ therefore \: we \: \: have \: \\ ( {x - 2})^{2} + (y - ( - 5)) {}^{2} = ({16})^{2} \\ ({x - 2})^{2} + ( {y + 5})^{2} = 256$
HOPE THIS HELPS!

8 0

2 years ago

Audrey, an astronomer is searching for extra-solar planets using the technique of relativistic lensing. Though there are believe

Stolb23 [73]

Answer:

Step-by-step explanation:

The model $N (t)$ , the number of planets found up to time $t$ , as a Poisson process. So, the $N (t)$ has distribution of Poison distribution with parameter $(\lambda t)$

a)

The mean for a month is, $\lambda = \frac{1}{3}$ per month

$E[N(t)]= \lambda t\\\\=\frac{1}{3}(24)\\\\=8$

(Here. t = 24)

For Poisson process mean and variance are same,

$Var[N (t)]= Var[N(24)]\\= E [N (24)]\\=8$

(Poisson distribution mean and variance equal)

The standard deviation of the number of planets is,

$\sigma( 24 )] =\sqrt{Var[ N(24)]}=\sqrt{8}= 2.828$

b)

For the Poisson process the intervals between events(finding a new planet) have independent exponential distribution with parameter $\lambda$ . The sum of $K$ of these independent exponential has distribution Gamma $(K, \lambda)$ .

From the given information, $k = 6$ and $\lambda =\frac{1}{3}$

Calculate the expected value.

$E(x)=\frac{\alpha}{\beta}\\\\=\frac{K}{\lambda}\\\\=\frac{6}{\frac{1}{3}}\\\\=18$

(Here, $\alpha =k$ and $\beta=\lambda$ )

C)

Calculate the probability that she will become eligible for the prize within one year.

Here, 1 year is equal to 12 months.

P(X ≤ 12) = (1/Г (k)λ^k)(x)^(k-1).(e)^(-x/λ)

$=\frac{1}{Г (6)(\frac{1}{3})^6}(12)^{6-1}e^{-36}\\\\=0.2148696\\=0.2419\\=21.49%$

Hence, the required probability is 0.2149 or 21.49%

5 0

3 years ago

Cada par de numeros esta a razon de 2:3

german

(0,8)+(7,-52) eso es la problema

4 0

3 years ago

Which expression can you substitute in the indicated equation to solve 3x − y = 5, x + 2y = 4 ?

Alenkasestr [34]

Answer:

3x−y=5;x+2y=4

x=2 and y=1

Step-by-step explanation:

7 0

3 years ago

To make the swim team Pedro must swim 400 m in less than seven minutes Pedro where the first 200 minutes in 2.86 minute he swam

MArishka [77]

Answer:

No he didnt make the team

Step-by-step explanation:

2.86 + 3.95= 6.81

so he swam 400 meters in 6min and 81 sec but theirs 60 sec in every min so realy he swam it in 7 min and 21 sec

5 0

3 years ago