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=(4)/(3)\pi r^3`

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

`(6*10^(-2))/(2)=3*10^(-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=(4)/(3)(3.14)(3*10^(-2))=0.1256 \\ \\ 0.1256=1.256*10^1 \end{gathered}`

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

`V\approx1.3*10^1\text{ cubic meters}`