Answer
The correct answer is (b) 2d
Work Step by Step
Let $d$ be the diameter of a sphere.
Then the radius $r$ is $d/2$.
Note that $d = 2r$.
The volume of the sphere is $V = \frac{4}{3}\pi r^3$
We need to make a new sphere with a volume $V_2$ that is 8 times the original volume. Let $r_2$ be the radius of this new sphere.
$V_2 = 8\times V$
$\frac{4}{3}\pi r_2^3 = 8 \times \frac{4}{3}\pi r^3$
$r_2^3 = 8\times r^3$
$r_2 = \sqrt[3] {8\times r^3} = 2r$
The new diameter is $2\times (2r)$ which is $2d$
The correct answer is (b) 2d
