All categories

3 years ago

Find the volume of the cylinder shown. Use 3.14 for pi. Round your answer to the nearest hundredth.

Mathematics

2 answers:

dmitriy555 [2]3 years ago

6 0

Answer: Volume of cylinder is 1846.32 cubic yd.

Step-by-step explanation:

Since we have given that

Height of a cylinder = 12 yard

Radius of a cylinder = 7 yard

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

$Volume=\pi r^2h\\\\Volume=3.14\times 7\times 7\times 12\\\\Volume=1846.32\ yd^3$

Hence, Volume of cylinder is 1846.32 cubic yd.

bearhunter [10]3 years ago

3 0

Answer:

1846.32 cubic yards

Step-by-step explanation:

You might be interested in

Lacy draws a diamond from a standard deck of 52 cards. Without replacing the first card, she then proceeds to draw a second card

Viktor [21]

Answer:

a) i) No

ii) Probability of drawing a diamond and then spade without replacement is 0.0637.

b) i) Yes

ii) Probability of drawing a diamond and then spade with replacement is 0.0625

Step-by-step explanation:

Part a) Without replacement:

i) Are these events independent?

No, because the both events are dependent. because a card taken out of the deck is not replaced back before taking out the other card so the chances of event occur change.

ii) Determine the probability of drawing a diamond and then a spade without replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond = 13/52

Probability of drawing a spade:

Total cards in deck after taking diamond = 52 -1 =51

Spades = 13

Probability of drawing a spade = 13/51

Probability of drawing a diamond and then spade = 13/52 * 13/51

= 169/2652

=0.0637

So, Probability of drawing a diamond and then spade without replacement is 0.0637

Part b) With replacements

i) Are these events independent?

Input Yes or No:

Yes, these events are independent because a card taken out of the deck is replaced back before taking out the other card so the chances of event occur doesn't change.

ii) Determine the probability of drawing a diamond and then a spade with replacement.

Probability of drawing a diamond and then spade = (Probability of drawing a diamond) * (Probability of drawing a spade)

Probability of drawing a diamond :

Total cards in deck = 52

Diamonds = 13

Probability of drawing a diamond = 13/52

Probability of drawing a spade:

Total cards in deck after replacing diamond = 52

Spades = 13

Probability of drawing a spade = 13/52

Probability of drawing a diamond and then spade = 13/52 * 13/52

= 169/2704

=0.0625

So, Probability of drawing a diamond and then spade with replacement is 0.0625

7 0

3 years ago

Which of the following is a reasonable estimated answer to the following problem?

bulgar [2K]

$989,867 \approx 1,000,000$
$999 \approx 1000$

$\implies \frac{989,867}{999} \approx \frac{1,000,000}{1000}$
$\frac{1,000,000}{1000} = 1000$

So the answer is approximately 1000.

4 0

3 years ago

Read 2 more answers

Which equation could be the first step in solving 4x+11/3=5x

ZanzabumX [31]

Move 5x to the left so it would turn into a negative 5x

4 0

3 years ago

Read 2 more answers

Ron deposits $2,000 into an account that receives 3.1% interest compounded continuously. How much money is in the account after

Alla [95]

In general, the continuous compounding interest formula is

$\begin{gathered} P(t)=Pe^{rt} \\ P\rightarrow\text{ initial amount} \\ t\rightarrow\text{ time} \\ r\rightarrow\text{ interest rate} \end{gathered}$

Therefore, in our case,

$P(t)=2000e^{0.031t}$

Set t=9 as shown below

$\Rightarrow P(9)=2000e^{0.279}\approx2643.615...$ <h2>The exact answer is 2000e^(0.279)</h2>

8 0

1 year ago

A piece of wire 30 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.

antiseptic1488 [7]

Answer:

a) 0 m

b) 16.8 m

Step-by-step explanation:

A piece of wire, 30 m long, is cut in two sections: a and b. Then, the relation between a and b is:

$a+b=30\\\\b=30-a$

The section "a" is used to make a square and the section "b" is used to make a circle.

The section "a" will be the perimeter of the square, so the square side will be:

$l=a/4$

Then, the area of the square is:

$A_s=l^2=(a/4)^2=a^2/16$

The section "b" will be the perimeter of the circle. Then, the radius of the circle will be:

$2\pi r=b=30-a\\\\r=\dfrac{30-a}{2\pi}$

The area of the circle will be:

$A_c=\pi r^2=\pi\left(\dfrac{30-a}{2\pi}\right)^2=\pi\left(\dfrac{900-60a+a^2}{4\pi^2}\right)=\dfrac{900-60a+a^2}{4\pi}$

The total area enclosed in this two figures is:

$A=A_s+A_c=\dfrac{a^2}{16}+\dfrac{900-60a+a^2}{4\pi}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}$

To calculate the extreme values of the total area, we derive and equal to 0:

$\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)a^2-\dfrac{60a}{4\pi}+\dfrac{900}{4\pi}\\\\\\\dfrac{dA}{da}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2a)-\dfrac{60}{4\pi}+0=0\\\\\\\left(\dfrac{1}{8}+\dfrac{1}{2\pi}\right)a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8\pi}\cdot a=\dfrac{15}{\pi}\\\\\\\dfrac{\pi+4}{8}\cdot a=15\\\\\\a=15\cdot \dfrac{8}{\pi+4}\approx 16.8$

We obtain one value for the extreme value, that is a=16.8.

We can derive again and calculate the value of the second derivative at a=16.8 in order to know if the extreme value is a minimum (the second derivative has a positive value) or is a maximum (the second derivative has a negative value):

$\dfrac{d^2A}{da^2}=\left(\dfrac{1}{16}+\dfrac{1}{4\pi}\right)(2)-0=\dfrac{1}{8}+\dfrac{1}{2\pi}>0$

As the second derivative is positive at a=16.8, this value is a minimum.

In order to find the maximum area, we analyze the function. It is a parabola, which decreases until a=16.8, and then increases.

Then, the maximum value has to be at a=0 or a=30, that are the extremes of the range of valid solutions.

When a=0 (and therefore, b=30), all the wire is used for the circle, so the total area is a circle, which surface is:

$A=\pi r^2=\pi\left( \dfrac{30}{2\pi}\right)^2=\dfrac{900}{4\pi}\approx71.62$

When a=30, all the wire is used for the square, so the total area is:

$A=a^2/16=30^2/16=900/16=56.25$

The maximum value happens for a=0.

3 0

3 years ago