Question

what is the volume of this sphere? round your answer to the nearest hundredth. cubic inches submit

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume of a sphere is \( V=\frac{4}{3}\pi r^{3} \), where \( r \) is the radius of the sphere.

Step2: Identify the radius

Given that the radius \( r = 6\) inches.

Step3: Substitute the radius into the formula

Substitute \( r = 6\) into \( V=\frac{4}{3}\pi r^{3}\), we get \( V=\frac{4}{3}\pi(6)^{3}\).
First, calculate \(6^{3}=6\times6\times6 = 216\).
Then \( V=\frac{4}{3}\pi\times216\).
\(\frac{4}{3}\times216=4\times72 = 288\). So \( V = 288\pi\).

Step4: Calculate the numerical value

Using \(\pi\approx3.14159\), then \( V\approx288\times3.14159\).
\(288\times3.14159=(300 - 12)\times3.14159=300\times3.14159-12\times3.14159\).
\(300\times3.14159 = 942.477\), \(12\times3.14159=37.69908\).
\(V\approx942.477- 37.69908=904.77792\approx904.78\) (rounded to the nearest hundredth).

Answer:

\(904.78\)