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labwork [276]
3 years ago
8

Sphere A has a diameter of 12 and is dilated by a scale factor of one half to create sphere B. What is the ratio of the volume o

f sphere A to sphere B?
Mathematics
1 answer:
Mrac [35]3 years ago
4 0

Answer:

VA/VB = 8

Step-by-step explanation:

You have a sphere A with diameter 12, that is, radius 6, which can be written as follow:

V_A=\frac{4}{3}\pi r_A^3=\frac{4}{3}\pi (6)^3=288\pi             (1)

The sphere A is dilated by a scale factor of one half to sphere B. Then, you have:

V_B=\frac{4}{3}\pi r_B^3=\frac{4}{3}\pi (\frac{6}{2})^3=36\pi       (2)

From the results of equation (2) and (1) you can calculate the ratio VA/VB:

\frac{V_A}{V_B}=\frac{288\pi}{36\pi}=8

The ratio of the volumes of both sphere A and B is 8

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R=8cm find the unknown length for a circle with the given dimension
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Use this and put in 8 for r C=2 \pi r

26.24

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3 years ago
Crunch Bunch cereal boxes come in two sizes. The mini cereal box of Crunch Bunch is a reduction of the standard box. A standard
Vladimir [108]

Answer: 10 inches.

Step-by-step explanation:

Hi, to answer this question we have to apply proportions (because both boxes are equivalent in measures).

Mini box: height 4 inches and width 3.2 inches

The proportion is: 4 in (height) / 3.2 in (width)

Standard box: height x inches and width 8 inches

x in (height) / 8 in ( width)

So:

x /8= 4/ 3.2

Solving for x:

x = (4/ 3.2) 8

x = 10 inches

Feel free to ask for more if needed or if you did not understand something.

5 0
3 years ago
Read 2 more answers
An employee put $5,000.00 in a retirement account that offers 9% interest compounded annually. The employee makes no additional
ZanzabumX [31]
<h3>Answer:</h3>
  1. $2693.12
  2. $2125.00
  3. B) The area of the field is 10.24 times the area of the playground
<h3>Step-by-step explanation:</h3>

1. Each year the balance is multiplied by 1.09, so after 5 years, the balance is multiplied by 1.09^5 ≈ 1.53862395. Subtracting the original invetment amount gives the value of the interest earned.

... 5000 × 1.53862395 - 5000 = 5000 × 0.53862395

... ≈ 2693.12 . . . . matches choice D

2. The interest earned is given by the formula ...

... I = Prt . . . . .  where P is the principal, r is the interest rate, and t is the time period.

Filling in the given numbers, you have ...

... I = 2500×0.085×10 = 2125 . . . . matches choice B

3. The product of length and width is the area. If both length and width are multiplied by 3.2, then the area is multiplied by 3.2×3.2 = 10.24. The appropriate choice is B.


5 0
3 years ago
Read 2 more answers
What is the measure of angle fsm
Bond [772]
92 it changes pipe walls, it's use to detect monitors.
fsm is an acronym
8 0
3 years ago
the frame of a picture is 28 cm by 32 cm outside and is of uniform width.What is the width of the frame if 192 cm2 of the pictur
natita [175]

Answer:

The width of the frame is equal to 8\ cm  

Step-by-step explanation:

Let

x-------> the width of the frame picture

we know that

(28-2x)(32-2x)=192    

896-56x-64x+4x^{2} =192

4x^{2}-120x+704=0  

Simplify

x^{2}-30x+176=0

The formula to solve a quadratic equation of the form ax^{2} +bx+c=0 is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

x^{2}-30x+176=0

so

a=1\\b=-30\\c=176

substitute in the formula

x=\frac{30(+/-)\sqrt{(-30)^{2}-4(1)(176)}} {2(1)}

x=\frac{30(+/-)\sqrt{196}} {2}

x=\frac{30(+/-)14} {2}

x=\frac{30+14} {2}=22\ cm  ----> this solution is not logic

x=\frac{30-14} {2}=8\ cm  

The width of the frame is equal to 8\ cm  

8 0
3 years ago
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