Calculate the volume of the following shapes. Use the approximation of pi.

1) A sphere with a radius of 4.5 cm
2) A cylinder with a radius of 2.1 cm and a height of 8.0 cm
3) A cone with a radius of 8.0 cm and a height of 2.0 cm

Please explain your work!

Answers

Answer 1
Note: I'm assuming that your teacher wants you to use the approximation pi = 3.14
-------------------------------------------------------
Problem 1)

Plug the value r = 4.5 into the formula below to find the approximate volume

V = (4/3)*pi*r^3
V = (4/3)*pi*(4.5)^3
V = (4/3)*pi*91.125
V = (4/3)*91.125*pi
V = 121.5*pi
V = 121.5*(3.14)
V = 381.51

So the approximate volume of this sphere is roughly 381.51 cubic cm

Note: we can write "cubic cm" as "cm^3"
-------------------------------------------------------
Problem 2)

The formula to use for the volume of a cylinder is
V = pi*r^2*h
where r is the radius and h is the height

In this case, we have r = 2.1 and h = 8.0

V = pi*r^2*h
V = pi*(2.1)^2*8.0
V = pi*4.41*8.0
V = pi*35.28
V = 35.28*pi
V = 35.28*(3.14)
V = 110.7792

The volume is roughly 110.7792 cubic cm
-------------------------------------------------------
Problem 3)

Now we use the formula
V = (1/3)*pi*r^2*h
which is the volume of a cone. Note how this is simply 1/3 the volume of the cylinder (with same radius and height)

Use r = 8.0 and h = 2.0

V = (1/3)*pi*r^2*h
V = (1/3)*pi*(8.0)^2*(2.0)
V = (1/3)*pi*64*2
V = (1/3)*pi*128
V = (1/3)*128*pi
V = (128/3)*pi
V = (128/3)*(3.14)
V = 133.973333

The approximate volume is 133.973333 cubic cm


Related Questions

Can someone solve these for me? I have no idea what I'm doing wrong. 19 points.

Answers

the first one is 0 and the second one is -2
Okay. I think this has to do with finding the spot of "y" with "x" at a spot on the graph.
1. With "x" being at -3, we can go on the graph and see where that particular position is. When x is at -3, y is at -6. y = -6.

2. This time, we're looking for one. With x being at 1, y would be at -2, because -2 is on the y-axis, while the x-axis is still 1. y = -2.

You and four friends go to johny rockets you split the bill each person pays 6.50 how much is the origanl bill

Answers

I think the answer is 26$ but I'm not sure

Describe the shapes that make the net for a cone?

Answers

It is a sector of a circle for the lateral surface and a circle for the top of the cone if it has one.

Graph the solution set to the inequality.


A.





B.


C.


D.

Answers

Answer:

this is the question from edgenunity i bet

alright first the question is

4(8-2y)4y+ less than or equal to  32 -8

we'll solve for Y by Isolating the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

y ≥ 2

the correct answer for me was A,

Step-by-step explanation:

The ratio of men to women working for a company is 7 to 4 . if there are 133 men working for the company, what is the total number of employees?

Answers

Let w be the number of women in the company.
We can write the ratio in dividing forms.
7/4 = 133/w
W = 76
So 76 + 133 is 209
So there r 209 workers in total

Why must eye protection be worn at all times in welding shop?

Answers

because of the ligting of the machine and you can go blind if theres no eye protection
The fumes are way to strong. Plus you'd have to rush to the hospital if something flew in your eyes or cut your eyes. Its always good to have protection.

HELP ME PLS!!!!!!!!.......

Answers

t = number of magazine subscriptions sold each week

"he sells at least 10 [magazine subscriptions]... each week" tells us that the smallest t can be is t = 10

Plug t = 10 into the function to get
f(t) = 48*t
f(10) = 48*10
f(10) = 480

The smallest amount of money Clarence earns is $480. This is the smallest value in the range.

The largest value in the range is 1200 because we plug t = 25 into f(t) to get
f(t) = 48*t
f(25) = 48*25
f(25) = 1200

Therefore the range is the set of multiples of 48 from 480 to 1200 (inclusive of both endpoints)

Answer: choice B

Side Note: Choice D is close to the answer but "the all whole numbers" needs to be "all multiples of 48"

the area of a rectangular swimming pool is 10x^2-19-15 the length is 5x+3 .what is the width of the pool?

Answers

2x-5 is the answer
hope it helps!
Hi There!


The answer is > 2x-5

Hope this helps please mark brainliest:)




2x-5

Which graph represents the function p(x) = |x – 1|?

Answers

Answer: The correct option is fourth option.

Explanation:

The given function is,

p(x)=|x-1|

The graph of the given function is a transformed form of f(x)=|x|.

The parent modulus function is,

P(x)=|x+a|+b

If a>0, then graph shifts left by a units and if a<0, then  graph shifts right by a units.

If b>0, then graph shifts upward by b units and if b<0, then  graph shifts downward by b units.

Since the value of a is -1 and value of b is 0, therefore the graph of f(x)=|x| shifts right side by 1 unit.

Hence the fourth option is correct.

Other way to choose the correct option is find the x intercept and y intercept.

Put x=0

P(x)=|0-1|= -1

So y-intercept is (0,-1)

Put p(x)=0

0=|x-1|

x=1

So, the x-intercept is (1,0).

From x and y-intercepts, we can say that the fourth option is correct.

Answer:

Fourth graph represent the  function p(x) = |x – 1|.

Step-by-step explanation:

Given :  Function p(x) = |x – 1|.

To find : Graph .

Solution : We have given that  Function p(x) = |x – 1|.

The graph of the given function is a transformed form of f(x)=|x|.

By the transformation rule f(x-h)  graph would be shifted to right by h units.

Since ,  grapf of function f(x)=|x| became shifted to 1 unit right.

Therefore , fourth graph represent the  function p(x) = |x – 1|.

Help me ! Giving Brainiest!

Answers

the range is the difference between the lowest value and highest value

 so you would subtract the lowest number from the highest number

Divide. Write your answer in simplest form.
eight divided by seven sixths

Answers

8 / (7/6)

8 x (6/7)

48/7  = 6.857

hope this helps

A cotton candy vendor has 30 cones of blue cotton candy to sell. If the blue cotton candy is 75% of the total number of cones, how many total cotton candy cones does he have?


Answers

40 cotton candy cones

simplify:  
30/75 (about this, just simplified version)=10/25=40/100

+10 is answer 

40 is final answer

Answer:

40

Step-by-step explanation:

because its just easy trust me it is !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! i just need points but fr fr its 40

What is the value of x?

Answers

2x+2 + 5x+3 = 180

7x+5 = 180

7x = 175

x = 175/7 = 25

x = 25

what’s three times the difference of a number and four is -9

Answers

Greetings!

We can translate this into an equation:
[tex]3(x-4)=-9[/tex]

Solve for x:
Distribute the Parenthesis.
[tex]3x-12=-9[/tex]
Add 12 to both sides.
[tex](3x-12)+12=(-9)+12[/tex]
[tex]3x=3[/tex]
Divide both sides by 3.
[tex](3x)/3=(3)/3[/tex]
The Answer Is:
[tex]x=1[/tex]

Hope this helps.
-Benjamin

Which operation will solve the equation?

m + 9 = 20

Question 2 options:

Add 9 to each side.


Subtract 9 from each side.


Add 20 to each side.


Subtract 20 from each side.

Answers

Subtract 9 from each side.
Subtract 9 from each side.

9x100+2x10+3x0.1+7x0.001

Answers

(9 * 100) + (2 * 10) + (3 * 0.1) + (7 * 0.001) =

920.307

Check whether the given number is a solution of the equation
6x+1-5x=7;2

Answers

6x + 1 - 5x = 7 when x = 2

To check this answer, you simply need to plug in 2 for x in the original equation.

6x + 1 - 5x = 7

6(2) + 1 - 5(2) = 7

Simplify.

12 + 1 - 10 = 7

Simplify.

13 - 10 = 7

Simplify.

3 = 7

3 ≠ 7 Therefore x does NOT equal 2.

~Hope I helped!~

The scale on a map of Virginia shows that 1 centimeter represents 30 miles. The actual distance from Richmond, VA to Washington, DC is 110 miles. On the map, how many centimeters are between the two cities? Round your answer to the tenth.

Answers

The ratio of cm to mi is 1/30, and we are looking for x/110. Since 1/30 = x/110, 30x=110.
x = 110/30 = 11/3 = 3.7 cm

Answer:

3.7 cm

Step-by-step explanation:

Simplify the expression 11x − (2x2 + 8x).

Answers

[tex]11x - (2x^2 + 8x)[/tex] 

[tex]11x-2x^2-8x[/tex] 

[tex](11x-8x)-2x^2[/tex] 

[tex]3x-2x^2[/tex]

Find the square numbers between 50 and 100

Answers

64, 81, and 100 are square numbers in between 50 and 100

Five times the sum of a number and seven is thirty. find the number.

Answers

first you have to write the equation...(x+7)5=30
then solve; so, x= -1

A tennis ball hit from the ground level into the air. Its height above the ground at the time can be modeled by the function h(t) = -16t² +160t. The height, h, is measured in feet above the ground and the time, t, is measured in seconds after the ball is hit. How long is the ball in the air?

Answers

h(t) = -16t^2 + 160t
The ball is in the air after t=0 and when it hits the ground again at
0 = -16t^2 + 160t
16t^2 = 160t  
t = 0 and 10 shows the ball is in the air 10 seconds..

Answer:

a

Step-by-step explanation:

When can an economy achieve price stability? An economy can achieve price stability when there is a _____ and stable inflation rate for a reasonably long period of time.
A. Low
B. High
C. Moderate

Answers

A. Low

The lower the inflation rate, the better

hope this helps
The answer to that is 

A. Low

If it takes 3 days for 10 workers to finish building one house, how many days will it take 15 workers to finish 4 houses?

Answers

a = house
3 days x 10 worker = a
a = 30 work unit
4a = 120 work unit
120 work unit = 15 workers * y days
y = 120/15 = 8 days

i hope this isn't too confusing 

At green deli employees earn double time for any hours worked in addition to their usual 40-hour week. Ester Klein worked 43 hours this week. Klein's regular hourly rate is $9.00 an hour. What is her total pay this week?

Answers

For the 40 hour week, they would be paid 40 multiplied by 9 which is 360. For the additional 3 hours they would be paid 18 dollars an hour, because its double.18 multiplied by 3 is 54. 360 + 54= 414. The answer is $414

Answer:

$414.00

Step-by-step explanation:

At green deli employees earn double time for their over time.

Klein's regular hourly rate = $9.00

So, her overtime rate = $9 × 2 = $18.00

Ester Klein worked 43 hours this week.

40 hours regular work + 3 hours overtime

Her total pay this week = (40 × 9) + (3 × 18)

                                       = 360 + 54

                                       = $414.00

Her total pay this week is  $414.00

A Flagpole is 28 ft high and the distance along the line of sight from the top of the flagpole to a person looking up at it is 35ft. What is the angle of depression from the top of the flagpole to the person?

Answers

arcsin(28/35) = 53.1

In order to receive a b in your english class, you must earn more than 350 points of reading credits. last week you earned 120 points. this week you earned 90 points. how many more points must you earn to receive a b or better in english?

Answers

120 + 90 = 210 points
350 - 210 = 140 OR
   351 - 210 = 141  (if it must be more than 350, you need at least 351 points total, or 141 more points, to get a grade B)

The perimeter of a rectangle is 112 cm. if the length is 30 cm, how wide is the rectangle?

Answers

P = 2l + 2w
112 = 2(30) + 2w
112 = 60 + 2w
52 = 2w
26 = w
The width is 26 centimeters

The sum that represents the number of tickets sold if 35 tickets were sold on monday, half of the remaining tickets were sold on tuesday , and 14 ticket were sold on wenesday

Answers

X=35+{0.5 *(X-35)} +14

A peer is having difficulty finding angle measures using trigonometric ratios in a right triangle. Create an example to demonstrate how to do this and be sure to address using the reciprocal relationships (cosecant, secant, cotangent too)

Answers

Please see diagram:
A right triangle has 3 main trigonometric ratios. These ratios are the relationships between different sides of the triangle, how large one side is compared to the other side. If you have every angle, in degrees, of a triangle, then you can figure out the relation between the lengths of the three sides. Additionally, you can figure out the value of the angles, given the sides of the triangle. 
In the diagram, we are interested in the trigonometric ratios with respect to angle a

You see in the diagram that sine, cosine, and tangeant are described as their ratios: (one way to remember: SohCahToa
sine = opposite / hypotenuse      
cosine = adjacent / hypotenuse                 
tangeant = opposite / adjacent. 

cosecant, secant, and cotangents are just the reciprocals of these ratios:
cosecant = 1 / sin 
secant = 1 / cosine
cotangeant = 1 / tangeant

Final answer:

To find angle measures using trigonometric ratios, such as sine, cosine, and tangent, as well as their reciprocals (cosecant, secant, and cotangent), use SOHCAHTOA to relate the sides of the triangle to the angle. Utilize the inverse trigonometric functions (like arccos) on your calculator to find the angle's measure from the ratio you have calculated with sides of the triangle.

Explanation:

To find angle measures using trigonometric ratios in a right triangle, we can use the mnemonic SOHCAHTOA, which stands for Sine equals Opposite over Hypotenuse, Cosine equals Adjacent over Hypotenuse, and Tangent equals Opposite over Adjacent. Let's create an example:

Suppose we have a right triangle with a hypotenuse (h) of 10 units and an adjacent side (x) to angle theta of 8 units.

To find the cosine of angle theta, we use the ratio Cos(theta) = x/h. Thus, Cos(theta) = 8/10 = 0.8.

To determine the actual measure of angle theta, we use the inverse cosine function: theta = arccos(0.8), which gives us the angle's measure in degrees or radians.

For the reciprocal, secant (Sec) is simply the inverse of cosine: Sec(theta) = 1/Cos(theta) = 10/8 = 1.25.

If we needed to use the cotangent, which is the reciprocal of the tangent, we would first need to find the opposite side (y) using the Pythagorean theorem and then use the ratio Cot(theta) = x/y.

It's essential to understand these relationships and how to use the inverse functions to find the angle measures in a right triangle. Reciprocal relationships involve the use of cosecant (Csc), which is 1/Sin(theta), secant (Sec), and cotangent (Cot), which is 1/Tan(theta). Always make sure your calculator is set to the correct unit (degrees or radians) before calculating the angle.

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