Question

Approximate the volume of the sphere.LE6 x 10-^2 mUse 3.14 for T and round the first factor in scientific notation to the nearest tenth.Enter the correct answer in the boxes.

Answer 1

In this problem, we want to find the volume of a sphere with the given radius in scientific notation.

The volume formula we will use is

$V=\frac{4}{3}\pi r^3$

Since we are given the diameter, we need to start by dividing it by 2 to get the radius:

$\frac{6\times10^{-2}}{2}=3\times10^{-2}$

Substituting that into our formula, we can simplify and apply the laws of exponents. Be sure to include 3.14 for π:

$\begin{gathered} V=\frac{4}{3}(3.14)(3\times10^{-2})=0.1256 \\ \\ 0.1256=1.256\times10^1 \end{gathered}$

Since we are rounding our scientific notation to the nearest tenth:

$V\approx1.3\times10^1\text{ cubic meters}$