Sphere A has a diameter of 2 and is dilated by a scale factor of 3 to create sphere B. What is the ratio of the volume of sphere A to sphere B?A 2:6
B 4:36
C 1:3
D 1:27
Answers
Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. The correct option is D.
What are Scaled figures?
Scaled figures are zoomed in or zoomed out (or just no zoom) versions of each other. They have scaled versions of each other, and by scale, we mean that each of their dimension(like height, width etc linear quantities) are constant multiple of their similar figure.
So, if a side of a figure is of length L units, and that of its similarfigure is of M units, then:
where 'k' will be called a scale factor.
The linear things grow linearly like length, height etc.
The quantities which are squares or multiple linear things twice grow by the square of the scale factor. Thus, we need to multiply or divide by k²
to get each other corresponding quantities from their similar figures' quantities.
So the area of the first figure = k² × the area of the second figure
Similarly, increasing product-derived quantities will need increased power of 'k' to get the corresponding quantity. Thus, for volume, it is k cubed. or
The volume of the first figure = k³ × volume of the second figure.
It is because we will need to multiply 3 linearquantities to get volume, which results in k getting multiplied 3 times, thus, cubed.
Given that the diameter of sphere A is 2 units, it is dilated by a scale factor of 3 to create sphere B. Therefore, the diameter of sphere B is,
Diameter of sphere B = 3 × Diameter of sphere A
= 3 × 2 units
= 6 units
Now, the ratio of diameters of the sphere and the volume of the sphere can be written as,
Hence, the correct option is D.
Learn more about Scale Factors:
#SPJ2
Answer:
1:27
Step-by-step explanation:
I will use solve in terms of pi
Know that Original volume * scale factor cubed = new volume.
The scale factor is 3 and 3^3 is 27,
Therefore the ratio is 1:27
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Answer:
10x² - 48y² - 11x + 2y - 74xy
Step-by-step explanation:
(-x+8y)+(-10x-6y)(−x+8y)+(−10x−6y)
Rearranging,
=> - x - 10 x + 8y - 6y + (-10x-6y)(−x+8y)
=> - 11x + 2y + 10x² - 48y² + 6xy - 80xy
=> 10x² - 48y² - 11x + 2y - 74xy
Answers
Answer:
In order to properly answer this, we need to know the measurement of the pool in meters
Step-by-step explanation:
Answer: what are the numbers?
Step-by-step explanation:
Answers
3D + 12
___ ___
3 3
so, hypo thinking once 3 is divided should leave you with . ↓
D = 4 cause once you do all the cancellations it basically leads 2 D then you have to divide →→ 12/3 → 3·4 or 4·3 either way it equals 12 sooo just do the math and you will come up with ...............................↓
-Hope this helped you any if not so comment right answer D=4 :)
a = –1, b = 1, c = –2
a = 1, b = –1, c = 2
a = –1, b = 1, c = 2
Answers
B = -1
C = 2 is your answer if you solve the equation.
(And don't worry I didn't copy this person's answers. I just solved it out in my head that's all).
x² - x + 2 = 0
Comparing the given equation to Ax² + Bx + C = 0, we get,
A = 1
B = -1
C = 2
Answers
Answer:
3.5 would be halfway of 3 and 4.
Answer:3.5
Step-by-step explanation:
3.5 is half of 3 and 4
Answers
Move all the numbers with variable on ones side
-7 = 5t - 3t
Combine like factors
-7 = 2t
Solve for t
-7/2 = t
After solving for t, you plug the answer into the equation you want to solve.
6 (-7/2) = -21
6*-7 = -42
-42/2 = -21
The answer is -21