Question

a sphere has a volume of 904.32 cm³. what is its radius? use π ≈ 3.1
a. 4 cm
b. 6 cm
c. 5 cm
d. 7 cm

Explanation:

Step1: Recall the volume formula for a sphere

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

Step2: Substitute the given values into the formula

We know \(V = 904.32\mathrm{cm}^{3}\) and \(\pi\approx3.14\). So, \(904.32=\frac{4}{3}\times3.14\times r^{3}\).
First, simplify \(\frac{4}{3}\times3.14=\frac{12.56}{3}\). Then the equation becomes \(904.32=\frac{12.56}{3}r^{3}\).
Multiply both sides by \(3\) to get \(904.32\times3 = 12.56r^{3}\), i.e., \(2712.96=12.56r^{3}\).

Step3: Solve for \(r^{3}\)

Divide both sides by \(12.56\): \(r^{3}=\frac{2712.96}{12.56}=216\).

Step4: Solve for \(r\)

Take the cube - root of both sides. Since \(r^{3}=216\), then \(r = \sqrt[3]{216}\). And \(\sqrt[3]{216}=6\) (because \(6\times6\times6 = 216\)).

Answer:

b. \(6\mathrm{cm}\)