Question

a company sells snow globes made out of glass that are in the shape of hollow spheres. mariam measures the outer diameter of a snow globe to be 30 cm. if the glass has a thickness of 0.25 cm, find the total volume of glass that makes up the globe. round your answer to the nearest hundredth if necessary. (note: diagram is not drawn to scale.)

Explanation:

Step1: Calculate the outer radius

The outer diameter \(d_{outer}=30\) cm, so the outer radius \(r_{outer}=\frac{d_{outer}}{2}=\frac{30}{2} = 15\) cm.

Step2: Calculate the inner radius

The thickness of the glass is \(t = 0.25\) cm. So the inner radius \(r_{inner}=r_{outer}-t=15 - 0.25=14.75\) cm.

Step3: Use the formula for the volume of a hollow sphere

The volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). The volume of the glass \(V = V_{outer}-V_{inner}\), where \(V_{outer}=\frac{4}{3}\pi r_{outer}^{3}\) and \(V_{inner}=\frac{4}{3}\pi r_{inner}^{3}\).

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Answer:

\(516.21\) \(cm^{3}\)