Question

1. . if a sphere has a volume of 2144.7 in³, what is the length of its radius?

Explanation:

Step1: Recall the volume formula of a sphere

The volume \( V \) of a sphere is given by the formula \( V=\frac{4}{3}\pi r^{3} \), where \( r \) is the radius of the sphere. We know the volume \( V = 2144.7\space in^{3}\), and we need to solve for \( r \).

Step2: Rearrange the formula to solve for \( r \)

First, we can multiply both sides of the equation \( V=\frac{4}{3}\pi r^{3} \) by \( \frac{3}{4\pi} \) to isolate \( r^{3} \). So we get \( r^{3}=\frac{3V}{4\pi} \).

Step3: Substitute the given volume into the formula

Substitute \( V = 2144.7\) into the formula for \( r^{3} \). We know that \( \pi\approx3.14 \), so:

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Step4: Solve for \( r \)

Since \( r^{3}\approx512 \), and we know that \( 8^{3}=512 \) (because \( 8\times8\times8 = 512\)), so \( r=\sqrt[3]{512}=8 \).

Answer:

The radius of the sphere is \( 8 \) inches.