Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B. What is the ratio of the volume of sphere A to sphere B?

8 : 1

Step-by-step explanation:

From the above question, we are given the following parameters

Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B.

Volume of a sphere = 4/3πr³

For Sphere A , diameter = 6

Radius = Diameter ÷ 2 = 6÷ 2 = 3

Volume of Sphere A = 4/3 × π × 3³

= 113.09733553 cubic units

Approximately = 113.1 cubic units

We were given a scale factor (k) of 2

Because we are dealing with volume, the scale factor will be cubed

In order to find the Volume of the sphere B

k³ = Volume of Sphere A/ Volume of Sphere B

2³ = 113.1 / Volume of Sphere B

Volume of Sphere B = 113.1/ 2³

= 14.1375 cubic units.

The ration of the Volume of Sphere A to Sphere B

Sphere A: Sphere B

113.1 : 14.14

= 8: 1

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation: