Question

A sphere is dilated by a scale factor of 5/2 to create a new sphere. How does the volume of the new sphere compare with the volume of the original sphere?

A) The volume of the new sphere is 2.5 times the volume of the original sphere.
B) The volume of the new sphere is 7.5 times the volume of the original sphere.
C) The volume of the new sphere is 2.5^2 times the volume of the original sphere.
D) The volume of the new sphere is 2.5^3 times the volume of the original sphere.

Answer 1

D D D D D D D !The answer to this question that you are trying to ask is d. say the sphere radius is one, if we did 4/3 of 1 cubed x 3.14, because the formula for volume is 4/3 pi R cubed, that would leave us with around 4.1., if you would take 1 times 2.5 cuz we're dilating, then you would have 4/3 of 2.5 cubed x 3.14. Now, the answer to that is around 10.46. Now, divide 10.46 bye 4.1. To get an answer of about 2.55, and remember were rounding, so if we did the exact math it would equal 2.5. so that would make it a, and I hope that you read this whole thing otherwise you just wasted all of those points... Evil Emoji evil emoji...

Answer 2

`\text{Volume of new sphere=}(2.5)^3* \text{Volume of original cube}`

Option D is correct

Explanation:

`\text{Given that a sphere is dilated by a scale factor of }(5)/(2)\text{ to create a new sphere}`

we have to compare the volume of two sphere.

`\text{As the sphere is dilated by a scale factor of }(5)/(2)=2.5`

which implies radius of sphere becomes 2.5 times

`\text{Volume of sphere=}(4)/(3)\pi r^3`

As the radius of new sphere=2.5r

∴
`\text{Volume of new sphere=}(4)/(3)\pi (2.5r)^3=2.5^3((4)/(3)\pi r^3)`

`\text{Volume of new sphere=}(2.5)^3* \text{Volume of original cube}`

Hence, option D is correct.