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Dafna1 [17]
2 years ago
9

A sphere with a radius of 6cm has the same volume as a cylinder with a height of 4.5cm. What is the radius of the cylinder

Mathematics
1 answer:
yawa3891 [41]2 years ago
4 0
Short answer: r = 8
Remark
The easiest way to do this is to solve the sphere's volume in terms of pi. When you do this, you can equate that to the formula for a cylinder and cancel the pi values. 

Step One
Find the volume of the sphere.

<em>Givens</em>
r = 6 cm

<em>Formula</em>
V = (4/3) pi r^3

<em>Sub and Solve</em>
V =  4/3 pi * 6^3
V = 288 * pi

Step two 
Find the radius of the cylinder

<em>Givens</em>
V = 288* pi cm^3
h = 4.5 cm

<em>Formula</em>
V = pi r^h

<em>Sub and solve</em>
288 pi cm^3 = pi r^2 * 4.5    Divide both sides by pi
288 cm^3 = 4.5 r^2              Divide both sides by 4.5
388 / 4.5 = r^2
64 = r^2                                Take the square root of both sides.
r = square root( 64)
r = 8 <<<<< Answer

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Which diagram best shows how fraction bars can be used to evaluate 1/2 divided by 1/4?
Helga [31]

Answer:

the second one

Step-by-step explanation:

2 halves make a whole. 1/2 + 1/2

4 fourths make a whole. 1/4 + 1/4 + 1/4 + 1/4

a half of a fourth is an eighth. 1/4 ÷ 1/2 = 1/8

3 0
2 years ago
The answer and how to do it
inessss [21]
Alright, here is how to do it:
First you are going to want to multiply 4x4. [That is Dino's Charges for 4 Sandwiches.] So once you've done that, you should get 16

Now, you're going to want to multiply 8x4. [That is Carla's charges for 4 Sandwiches.] So once you've done that, you should get 24.

Now, to find the difference you will have to subtract them. 24-16 = 18.
Now that we've done this we now know your answer is:
Carla's sandwiches cost more than Dino's sandwiches. The difference is 18 dollars.
-------------------------
I hope I helped, if I did; please give me brainliest. :)
4 0
2 years ago
For a statistics class project, a college student randomly samples 75 men who exercise at a gym regularly and 68 women who exerc
pav-90 [236]

Answer:

Step-by-step explanation:

The record of the statistics and the summary statistics which are the missing files in the question are attached below.

From the given information:

The null hypothesis and the alternative hypothesis can be represented by :

\mathbf{H_o:} There is no difference between the average time  spend by men and women at gym each week

\mathbf{H_i:} The average time  spend by men is greater than the average time spend by women at the gym each week

From the summary statistics in the attached file below:

The p-value = 0.3253

Level of significance = 5% = 0.05

Therefore; it is obvious that the p-value is greater than the level of significance  i.e (0.3253 > 0.05)

Hence; there is no enough evidence to reject the null hypothesis

CONCLUSION: We conclude that the mean number of minutes exercised per week is larger for men than women at the  this gym.

6 0
3 years ago
The table shows four numbers. -34<br>-0.4 0.4 ​
kvv77 [185]

Answer:

What do you have to do with the numbers

3 0
3 years ago
A ball is projected in to the air. Its height at time t is given by the equation
Ksju [112]
The equation gives the height of the ball. That is, h is the height of the ball. t is the time. Since we are looking for the time at which the height is 8 (h=8), we need to set the equation equal to 8 and solve for t. We do this as follows:

h=-16 t^{2} +60t+1
8=-16 t^{2} +60t+1
16 t^{2} -60t-1+8=0
16 t^{2} -60t+7=0

This is a quadratic equation and as it is set equal to 0 we can solve it using the quadratic formula. That formula is:
t= \frac{-bplus minus \sqrt{ b^{2}-4ac } }{2a}
You might recall seeing this as "x=..." but since our equation is in terms of t we use "t-=..."

In order to use the formula we need to identify a, b and c.
a = the coefficient (number in front of) t^{2} = 16.
b = the coefficient of t = -60
c = the constant (the number that is by itself) = 7

Substituting these into the quadratic formula gives us:
t= \frac{-(-60)plus minus \sqrt{ (-60)^{2}-4(16)(7) } }{2(16)}
t= \frac{60plus minus \sqrt{3600-448 } }{32}
t= \frac{60plus minus \sqrt{3152 } }{32}

As we have "plus minus" (this is usually written in symbols with a plus sign over a minus sign) we split the equation in two and obtain:
t=  \frac{60+56.1426}{32} =3.63
and
t=  \frac{60-56.1426}{32} =.12

So the height is 8 feet at t = 3.63 and t=.12

It should make sense that there are two times. The ball goes up, reaches it's highest height and then comes back down. As such the height will be 8 at some point on the way up and also at some point on the way down.


3 0
3 years ago
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