A sphere has a radius of 4 inches. Determine the effects on the surface area and volume of a sphere when the radius is changed.
Answers
Answer:
Step-by-step explanation:
The surface area of a sphere is given by
A=4πr^2
The volume is
V = (4/3)πr^3
At r = 4":
A = 64π in^2
V = 85.3π in^3
At r = 5" (a 25% increase in r)
A = 100π in^2 (a 156.25% increase)
V = 167π in^3 ( a 195.8% increase)
We can show the ratio of these two measures by dividing the Volume by the Area:
V/A = ((4/3)πr^3/(4πr^2))
V/A = (1/3)r
For the 2 examples (4" and 5"), V/A is:
4": (85.3π in^3)/(64π in^2) = 1.33 [(1/3)r = 4/3 = 1.33]
5": (167π in^3)/(100π in^2) = 1.67 [(1/3)r = 5/3 = 1.67]
V/A = (1/3)r
Since Volume is a function of r^3 and Area is related to r^2, Volume will always increase faster, by a ratio of 1/3 r.
Related Questions
PLEASE EXPLAIN THE WORK WHEN YOU ANSWER FOR ME PLEASE
solve each equation:
1: |b-6|=1
2:|b+2|=7
Answers
Answer:
Step-by-step explanation:
theres 2 possible solutions for each equation and each one is right
or for dummies, just reverse the +/- inside the l x +/- y l. and make 2 different equations the first with a + and the second with a -
1. lb-6l = 1
b - 6 = 1
b = 7
-----------
b + 6 = 1
b = -5
--------------
2. lb+2l=7
b + 2 = 7
b = 5
--------------
b - 2 = 7
b = 9
---------------
How do you solve for x
3x^2 = -24x
Answers
[tex]3x^2 = -24x \\\\\implies 3x^2 +24x =0\\\\\implies x^2 +8x = 0\\\\\implies x(x+8) =0\\\\\implies x =0~~ \text{or}~~ x = -8[/tex]
Step-by-step explanation:
3x² = -24x
Divide through by x
3x = -24
x = -24/3
x = -8
Mrs. Letting brought 40 cookies to school. Mrs. Letting's class ate 1/2 of the cookies and Mrs. Kim's class ate 1/4 of the cookies. How many cookies are left?
Answers
Explanation:
There were 40 cookies to start with. If Mrs. Lettings class at 1/2 of the cookies, there are now 20 cookies left. Mrs Kim’s class then ate 1/4, because 1/4 of 40 is 10, then they ate 10 cookies. So there are now 10 cookies left
Using the slope and the y-intercept, graph the line represented by the following equation. Then identify the figure
showing that graph.
2x-y+4=0
Answers
solve pls brainliest
Answers
Answer:
$18.15
Step-by-step explanation:
45% of $33 = $14.85
$33 - $14.85 = $18.15
Translate the sentence into an equation four more than six times a number is 11
Answers
6x+4=11
(x is "a number")
Denise is buying four birthday cards for $11.16. Sales tax on the four cards is $0.68. Including sales tax, what is the cost of each card?
Answers
Answer:
$11.16 - $0.68 = $10.48 - price of four cards without tax
$10.48 : 4 = $2.62 - price of one card without tax
Cheers!
Answer:
the cost of each card including sales tax is 2.79
the cost of each card without sales tax is
11.16-0.68=10.48
10.48÷4=2.62
Step-by-step explanation:
6. What is the percent of increase from 10 to
12?
A. 20%
B. 25%
C. 30%
D. 33
33%
Answers
Answer:
A. 20%
Step-by-step explanation:
% Increase = 12−10/10x100
= 2/10x100
= 20%
Mark me as brilliant
A. 20%
Explanation: I bet u get it right
Pls Solve
Due today
For a grade
First will be Brainliest!
Answers
Select all of the given points in the coordinate plane that lie on the graph of the linear equation $$.
Answers
blank as 9 hundred is 9 thousand
Answers
Answer:
x = 10
Step-by-step explanation:
x × 900 = 9000
=> 900x = 9000
=> x = 10
A limousine cost 75,000 new but deprecates at rate of 23% per year what is the value of the limousine after five years
Answers
Answer:
$20,300.88
Step-by-step explanation:
First Year : 75,000x(1-23%)
Second Year: 75,000x(1-23%)x(1-23%)
=75,000x(1-23%)^2
Third Year : 75,000x(1-23%)x(1-23%)x(1-23%)
=75,000x(1-23%)^3
x Year : 75,000x(1-23%)^x (Analogical Reasoning)
Hence : Fifth year:75,000x(1-23%)^5 = 75000x(0.77)^5
23%=0.23 1-23%=1-0.23=0.77
Therefore Fifth Year: 75000x(0.77)^5=$20300.88
there are 364 people in town for a conference. They have to go from the airport to the hotel and travel 12 people in a van. How many vans are needed?
Answers
Total number of people = 364
Number of people in 1 van = 12
Number of vans required = ?
Number of vans required = 364 / 12
= 30.33
But there's a remainder, so for the remaining few people to go you'll need an extra van. So, you need 31 vans.
=》Answer = option C. 31
______
RainbowSalt2222 ☔
A butcher makes meatloaf by mixing hamburger which sells for a $1.89/lb and sausage which sells for $2.99/lb how many pounds of each should be used if he makes 30 lb of mix and sell it for $2.33/lb
Answers
Answer:
12 and 18
Step-by-step explanation:
please help me in question 31 only please and i’ll mark the correct answer as brainliest i promise
Answers
The equation should be 1.75x + 2y = 18.
If the question means how many combinations of eggs to make 18 ounces, then only 7 large eggs and 8 medium eggs or 9 large eggs satisfy the equation.
x = 8, y = 7 or x = 0, y = 9.
How would you write the quotient with a simplified fraction as a remainder?
Answers
Answer:
The answer is B) 851 ÷ 46 = [tex]18 \frac{1}{2}[/tex]
Step-by-step explanation:
851 ÷ 46 = 18.5
[tex]18 \frac{1}{2}[/tex] = 18.5
18.5 = 18.5
Since both are the same result that means that option B is the correct answer.
I actually don’t understand this can someone please help?
Answers
Answer:
It's proportional when you have a straight line that goes through the origin, meaning (0,0), meaning x = 0 and y = 0, meaning: when x = 0, then y has to be = 0 too! That's obviously not the case here. You can see that the line hit the y axis way above 0. So this graph is not directly proportional to x.
Step-by-step explanation:
two one dollar bills are exchanged for 14 coins all of which are either quarters or dimes. how many dimes were in the exchange
Answers
The $2 are exchanged for 10 dimes and 4 quarters, which make 14 coins total.
Solve for Z:
4 > 5Z + 34
help me
Answers
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
Z < − 6
Interval Notation:
( − ∞ , − 6 )
Step-by-step explanation:
i need help: solve (4x^(6))^((3)/(2))
Answers
Answer:
(4x^{(6)})^{(\frac{(3)}{(2)})}
(4x(6))((2)(3))
Step-by-step explanation:
I think that's the answer
Someone plz help me :(
Answers
Answer:
B) 7 - 5x
Step-by-step explanation:
7 - 5x is the difference between the number 7 and the product of 5 and 'x'
The bag of potato chips has 25% more in the new package. the original package had 14 ounces. how many ounces are in the new bags?
Answers
Answer:
17.5 Ounces
Step-by-step explanation:
14/100=.14 .14x25=3.5 14+3.5=17.5
cos135° =
A.√2/2
B.-√2/2
C.-1/2
Answers
we have cos135° = -√2/2
so B is the correct answer
ok done. Thank to me :>
Select the two values of x that are roots of this equation.
x² + 2x - 4 = 0
O A. x= -1 - 15
B. x= -1+5
C. X=-1-215
D. x = -1+2-15
Answers
Answer:B and c
Step-by-step explanation:
On Tuesday, a restaurant serves iced tea to 24 of its 160 customers. What percent of the customers order iced tea
Answers
Answer:
15%
Step-by-step explanation:
24/160 = 0.15
0.15*100 = 15
find x.
please i need help!!
Answers
Step-by-step explanation:
sin45°=x/4√2
=> 1/√2 = x/4√2
=> x= 4√2/√2
=>x= 4.
hope this helps you.
The question is an illustration of right-angled triangles
The value of x is (b) 4
To calculate the value of x, we make use of the following sine ratio
[tex]\sin(45) = \frac{x}{4\sqrt 2}[/tex]
Multiply both sides of the equation by [tex]4\sqrt 2[/tex], to make x the subject of the formula
[tex]x = \sin(45) \times 4\sqrt 2[/tex]
Evaluate sin(45)
[tex]x = \frac{1}{\sqrt 2} \times 4\sqrt 2[/tex]
Cancel out the common factors
[tex]x = 4[/tex]
Hence, the value of x is (b) 4
Read more about right-angled triangles at:
https://brainly.com/question/16195823
+3 - (+7)
Can someone help pls!?
Answers
Answer:
Step-by-step explanation:
+3 - (+ 7) = 3 + (-7) = -4
Both integers have different sign. So, subtract and the result will have the sign of bigger number. Here bigger number is 7 and sign of 7 is (-). So, answer will be (-4)
Brandon has 32 stamps. He wants to display the in rows, with the same number of stamps in each row. how many different ways can he display the stamps? explain.
Answers
Answer:
You can put the stamps in three rows of 8 since 8 times 3 equal 32
Step-by-step explanation:
Hope it helps
Does anyone get this?
Answers
Dilation is the transformation that changes the size of a shape.
4 is a positive number so the shape will increase in size.
So after dilating every side by 4:
0,1
-0.5,0
1,0
We get
0,4
-2,0
4,0
Translate the sentence into an inequality.
A number w increased by 4 is greater than or equal to - 23.
Answers
Answer:
w + 4 ≥ -23
Step-by-step explanation:
"a number w": w
"increased by 4": + 4
"is greater than or equal to": ≥
"-23": -23
Put the parts of the equation together:
w + 4 ≥ -23
~
Answer: (x + 4) ≥ -23