7. Suppose a sphere has a volume of 3,000 cm3. Find the surface area.
The volume of a sphere: V= 4/3 pi r^3

Part I: Find the radius of the sphere by setting the volume equal to the formula above. Show your work and round the radius to the nearest hundredth.

Part II: Use the radius you found in Part I with the surface area formula below to the find the surface area of the sphere. Show your work and round your answer to the nearest tenth.

The surface area of a sphere: SA= 4 pi r^2

Answers

Answer 1

Answer:

Part 1

[tex]\boxed{r = 8.9 \;cm}[/tex]

Part 2

[tex]\boxed{SA=995.4\;cm^2}[/tex]

Step-by-step explanation:

If r is the radius of a sphere

Volume of a sphere:
[tex]V = \dfrac{4}{3}\pi r^2[/tex]

Surface Area
[tex]SA = 4\pi r^2[/tex]

Part 1
We are given volume = 3,000 cm³

Setting this to volume to the equation for volume gives
[tex]3000 = \dfrac{4}{3} \pi r^3\\\\[/tex]

Multiplying both sides by 3/4 yields

[tex]\dfrac{3}{4}\cdot 3000 = \pi r^3\\\\2250 = \pi r^3\\\\r^3 = \dfrac{2250}{\pi}\\\\r^3 \approx 716.1972\\\\\\r = \sqrt[3]{716.1972} \\\\r = 8.947\\\\\\\textrm{Rounded to the nearest tenth:}\\\\\boxed{r = 8.9 \;cm}\\\\\text{(Answer\;Part 1)}\\[/tex]

Part 2

Using r = 8.9 cm we can compute the surface area SA using the formula for surface area

[tex]SA = 4\pi r^2\\\\SA = 4\pi (8.9)^2\\\\SA = 995.38\;cm^2\\\\\textrm{Rounded to the nearest tenth:}\\\\\boxed{SA=995.4\;cm^2}\\\\\textrm{(Answer Part 2)}[/tex]


Related Questions

Can you see the image I’m not sure if you can please let me know

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Answer:

you can't sorry

Step-by-step explanation:

ycucycycufycycycyc

Answer:

no I can't see

Step-by-step explanation:

please mark me as brainlist

What is the solution to the equation sqrt 2x+3 minus sqrt x+2=2? x =

Answers

Answer:

x= 1/4 or 0.25

Answer:

23

Step-by-step explanation:

on edg

Cash loan $100 20.0% 3 years $6 (100 x .2 x .3) $106 ($100 + $6) Big-screen TV $500 9.0% 4 years $ (500x $ College loan $13,000 4.5% 15 years $ $

Answers

Answer:

Cash loan = $160

Big screen TV = $680

College loan = $$21775

Step-by-step explanation:

Cash loan :

Loan amount or principal = $100

Interest rate, r = 20.0%

Time, t = 3 years

Using the relation :

Simple interest = Principal * rate * time

$100 * 0.2 * 3 = $60

Final amount = loan amount + interest on loan

Final amount = $100 + $60 = $160

Big Screen TV:

Principal = $500

Rate, r = 9.0%

Time, t = 4 years

Interest amount = (500 * 0.09 * 4)

Interest amount = $180

Final amount = principal amount + interest on loan

Final amount = $500 + $180 = $680

College loan

Principal, = $13,000

Rate, r = 4.5%

Time, t = 15 years

Interest amount = (13000 * 0.045 * 15)

Interest amount = $8775

Final amount = principal amount + interest on loan

Final amount = $13000 + $8775 = $21775

x2 + 3x + 2 by x + 1​

Answers

Answer:

x²+3x+3

Step-by-step explanation:

hope it helps you

please mark me as brainlist

5x+2 x x+1
5x+2x+1
7x + 1

Determine the slope of the line

Answers

Answer:

2 !!

Step-by-step explanation:

use RISE/RUN !! you would go up from the 1 point, on the y axis !! from there, ud go up 2, then to the right 1, so ur slope is 2/1 .... which is 2 !!

i hope this helped !

funny corona-virus meme

Answers

Answer:

lol thats funny

Step-by-step explanation:

hahahahahahahahahahahahahahahahahahahahahahahaha!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! That is funny;)

PLEASE HELP,, A home decorator is adding new flooring to a living room using the blueprint shown.



image



What are the actual length and width of the living room? Show your work.

A.
7ft, 6ft

B.
14 ft, 10ft

C.
10ft, 8ft

D.
20ft, 16ft

Answers

The answer is 10 and 8 feet I hope you do good on this

Answer: 20ft, 16ft

Step-by-step explanation:

Because 0.5in=2ft, you would divide the length (5in) and the width (4) both by 0.5. Which give you 10 for the length and 8 for the width. Then you multiply both of those products by 2 and that gives you your answer. 20ft and 16ft. Hope this helps. :)

Which of the following is a situation in which an equation cannot be solved
using the quadratic formula?
A. The coefficient of the x-term is zero.
B. One term of the polynomial has a degree of 3.
C. The right-hand side of the equation is zero.
D. The coefficient of the XP-term is 1.

Answers

Answer:

B One term of the polynomial has a degree of 3

the answer for this problem is B

Jim rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travel in 3 days?

Answers

Answer:

48.72 km in 3 days.

Step-by-step explanation:

Given that,

A one-way trip is 8.12 kilometers.

We need to find the distance he travel in 3 days.

The distance traveled by Jim in one day to the bus and from school = 2(8.12) =  16.24 km

Distance traveled in 3 days = 3(16.24)

= 48.72 km

Hence, he will cover 48.72 km in 3 days.

Find the value of x.

Answers

Answer:

x=7

Step-by-step explanation:

Since the two lines, the transversal intersects are parallel we know that the angles are same-side interior. This means they are supplementary or add up to 180. Therefore, to solve add the two expressions and set them equal to 180, then solve with properties of equality.

14x+7+10x+5=180

First, add like terms

24x+12=180

Then, subtract 12 from both sides

24x=168

Next, divide both sides by 24

x=7

me Digão qual e a resposta​

Answers

Answer:

As somas estão abaixo

Step-by-step explanation:

a) 158

b) 2095

c) 2819

d) 9082

Eu espero que isso ajude :)

I need help with B. Do you I think this will mean the end of life on earth?

Please answer ASAP

Answers

Answer:

yes

Step-by-step explanation:

8 students in Mr. Webb's class got an A on the exit ticket. There are 25
students in his class total. What percent of students got an A?*

Answers

Answer:

32%

Step-by-step explanation:

To find the percentage, we have to multiply 25 and 8 by 4.

25x4 = 100

8x4 = 32

So, 8 out of 25 is 32%.

I NEED THIS RN AS FAST AS POSSIBLE! Your teacher decides to split the class into four equal groups with no more than five students in each group. that represents the number of students in the class.

Answers

Answer:

option 1 i think

Step-by-step explanation:

imma just take these 5 points back

What is the radius of a circle with a circumference of 81.64 feet.

Answers

Answer:

Step-by-step explanation:

Your answer

Circumference = 2 * π* r = 81.64

r = 12.99 → 13

Mark it as Brainlist answer. Follow me.

In the figure above, PQRS is a circle. If PQT and SRT
are straight lines, find the value of x.

Answers

Given:

PQRS is a circle, PQT and SRT  are straight lines.

To find:

The value of x.

Solution:

Since PQRS is a circle, PQT and SRT  are straight lines, therefore, PQRS isa cyclic quadrilateral.

We know that, sum of opposite angles of a cyclic quadrilateral is 180 degrees.

[tex]m\angle SPQ+m\angle QRS=180^\circ[/tex]

[tex]81^\circ+m\angle QRS=180^\circ[/tex]

[tex]m\angle QRS=180^\circ-81^\circ[/tex]

[tex]m\angle QRS=99^\circ[/tex]

Now, SRT  is a straight line.

[tex]m\angle QRT+m\angle QRS=180^\circ[/tex]             (Linear pair)

[tex]m\angle QRT+99^\circ=180^\circ[/tex]

[tex]m\angle QRT=180^\circ-99^\circ[/tex]

[tex]m\angle QRT=81^\circ[/tex]               ...(i)

According to the Exterior angle theorem, in a triangle the measure of an exterior angle is equal the sum of the opposite interior angles.

Using exterior angle theorem in triangle QRT, we get

[tex]m\angle PQR=m\angle QRT+m\angle QTR[/tex]

[tex]x=81^\circ+22^\circ[/tex]

[tex]x=103^\circ[/tex]

Therefore, the value of x is 103 degrees.

Find the area of the regular octagon.

Answers

Answer:

3*4

=12 sq. cm

= 12 cm²

Answer:

48cm^{2}

Step-by-step explanation:

[tex]A=4ah=4*4*3=48 cm^{2}[/tex]

Carl is deriving the quadratic equation by completing the square. His work at one of the steps is shown. x + b/na = + or - b^2-4ac. Carl is not sure what the value of n is. What value should he use to continue deriving the quadratic equation correctly? A. 1 B. 2 C. 3 D. 4

Answers

Answer:

the correct option is B. 2

Step-by-step explanation:

As given,

x + [tex]\frac{b}{na}[/tex] = ± √b²-4ac

⇒x = -[tex]\frac{b}{na}[/tex] ± √b²-4ac

As e know that the quadratic formula is

x = [tex]\frac{-b + or - \sqrt{b^{2} - 4ac } }{2a}[/tex]

So , by comparing with the formula

we get

n = 2

So, the correct option is B. 2

What is the value of x in the equation 6x + 3 + 4x =
(9 + 10x)?
Enter your answer in the box.
2
TIL
CON
4
6
7
8
CO

Answers

9514 1404 393

Answer:

  x = 3/10

Step-by-step explanation:

Given

  6x +3 +4x = 1/2(9 +10x)

We can collect term, then multiply by 2.

  10x + 3 = (1/2)(9 +10x)

  20x + 6 = 10x + 9 . . . . . . . multiply by 2

  10x = 3 . . . . . . . . . . . . . . . . subtract (6+10x)

  x = 3/10 . . . . . . . . . . . . . . . divide by 10

_____

Check

  6(3/10) +3 +4(3/10) = (1/2)(9 + 10(3/10))

  1.8 + 3 + 1.2 = 1/2(9 +3)

  6 = 6 . . . . . solution checks OK

1. In Mr. B's classroom, there are 20 students.
Twelve students got a B, one student got a C, and
the rest received an A. What percent of the class
received an'A?


Help please

Answers

Answer:

1.5%

Step-by-step explanation:

When is the graph of f (x) = 2x2 – 5x – 3 negative?​

Answers

9514 1404 393

Answer:

  -1/2 < x < 3

Step-by-step explanation:

First you need to find the x-intercepts. Since the leading coefficient is positive, you know the graph is decreasing through the left x-intercept, so will be negative between the x-intercept values.

  f(x) = 2x^2 -5x -3

  f(x) = 2x^2 -6x +x -3

  f(x) = 2x(x -3) +1(x -3)

  f(x) = (2x +1)(x -3)

The x-intercepts are the values of x that make these factors zero:

  2x +1 = 0   ⇒   x = -1/2

  x -3 = 0   ⇒   x = 3

The graph of f(x) is negative on the interval ...

  -1/2 < x < 3

What is the missing angle
120°
70°

Answers

Answer:

the measure of angle B is 50

Step-by-step explanation:

the measure on the other side of the 120 is 60

hope this helps!!

Dxfcv gnhbjmftvgyhgbyhgtyuvgyuibgiuguyvfgtyuik

Answers

Answer:

25.12 inches

Step-by-step explanation:

Find the missing length?

A. 18in
B. 6in
C. 2in
D. 36in

Answers

Answer:

B. 6in

Step-by-step explanation:

We can use the Pythagorean theorem [ a² + b² = c² ] to find the missing side.

8² + b² = 10²

64 + b² = 100

b² = 36

b = 6

Best of Luck!

Solve: -2x - 5 = -3
plz help me hurry

Answers

Answer:

x=-1

Step-by-step explanation:

-2x - 5 = -3

add 5 to both sides

-2x = 2

divide both sides by -2

x = -1

Answer:

x = -1

Step-by-step explanation:

-2x - 5 = -3

Same to both sides:

-2x = -3 + 5

Simplify:

-2x = 2

Divide by -2 on each side to isolate x:

x = -1

Let me know if you have any questions

Sara was cliff jumping. She was on a cliff 25 feet above sea level. She jumped into the sea and descended a total of 37 feet. How many feet below sea level did she travel? Justify your reasoning.

Answers

Answer:

12 feets below sea level

Step-by-step explanation:

Initial height = 25 feets above sea levwl

Total descent = 37 feets

Distance traveled below sea level = 37 feets - 25 feets = 12 feets

Hence, Sarah traveled 12 feets below sea level

SMART PEOPLE PLEASE TAKE THE TIME TO ANSWER THIS!!!!!!!!!

Answers

Answer:

40% ⋅ x = 35

x = 87.5

Step-by-step explanation:

To write an equation representing this situation, use the key words. 40% stays 40%. "Of" is the same as multiplication. "X" remains "x". "Is" is the same as equal to. 35 remains 35. So, the new equation you get is: 40% ⋅ x = 35.

To solve for "x", first turn the 40% into a decimal: 0.4. Now divide 0.4 from both sides to get: x = 87.5.

Note:

The dot "⋅", stands for the multiplication sign. I'm not using the "x" symbol for it because there is a variable x in the equation already.

Hope it helps!

select the correct choice and fill in the box to complete your choice. pls help!!!

Answers

Answer is Yes!! Hope this helps

What is the difference between the profits Mr. Brown's store earned in the first quarter and the third quarter?

Answers

Answer:

Hi we need a picture or a chart.

Step-by-step explanation:

Answer:

2,411.44

Step-by-step explanation:

P = 100 - 20 cos (8πt/3) That's (8 pi t /3) where t is the time (in seconds). What is the period of the model? Discuss what the period represents in the context of this model.

Answers

Answer:

The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.

Step-by-step explanation:

Cosine is a trigonometric function and trigonometric functions are characterized by having a periodical behavior. The period is the time needed for the function to cover an angle of [tex]2\pi[/tex] radians. By this approach we find that:

[tex]\frac{8\pi\cdot t}{3} = \frac{2\pi\cdot t}{T}[/tex] (1)

Where:

[tex]t[/tex] - Time, measured in seconds.

[tex]T[/tex] - Period, measured in seconds.

Then, we solve (1) for [tex]T[/tex]:

[tex]\frac{8}{3} = \frac{2\pi}{T}[/tex]

[tex]T = \frac{6\pi}{8}\,s[/tex]

[tex]T = \frac{3\pi}{4}\,s[/tex]

The period of the model is [tex]\frac{3\pi}{4}[/tex] seconds. The period represents the time needed for the function to complete one cycle.

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