Question

a company sells snow globes made out of glass that are in the shape of hollow spheres. nolan measures the outer diameter of a snow globe to be 30 cm. if the glass has a thickness of 0.5 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: Find outer radius

The outer diameter is 30 cm, so outer radius \( R = \frac{30}{2}=15 \) cm.

Step2: Find inner radius

Glass thickness is 0.5 cm, so inner radius \( r = 15 - 0.5 = 14.5 \) cm.

Step3: Volume of glass (hollow sphere)

The formula for the volume of a hollow sphere is \( V=\frac{4}{3}\pi(R^{3}-r^{3}) \).
Substitute \( R = 15 \) and \( r = 14.5 \):
\[

$$\begin{align*} V&=\frac{4}{3}\pi(15^{3}-14.5^{3})\\ &=\frac{4}{3}\pi(3375 - 3057.625)\\ &=\frac{4}{3}\pi(317.375)\\ &\approx\frac{4}{3}\times3.1416\times317.375\\ &\approx 1329.45 \end{align*}$$

\]

Answer:

\( 1329.45 \)