Question

A jeweler makes beads for a bracelet by melting silver into spherical molds. Each mold has a diameter of $1$ centimeter. After the silver hardens, the jeweler drills a small cylindrical hole through the center of the bead for the chain as shown. The drill bit has a diameter of $4$ millimeters. If the jeweler strings a total of $15$ beads on an elastic band, what is the approximate volume of silver, in cubic centimeters, on the bracelet?

Note: There are $10$ millimeters in $1$ centimeters.
Note: The volume is approximate because the top and bottom of the cylindrical piece that is drilled out is slightly curved.

• A. $\frac{19}{150}\pi$
• B. $\frac{1}{6}\pi$
• C. $\frac{19}{10}\pi$
• D. $\frac{5}{2}\pi$

Answer 1

The correct option is C $\frac{19}{10}\pi$

Solution:

Given that:

Diameter of the silver mold $=1cm$

Radius of the silver mold $=0.5cm$

Diameter of drill bit $=4mm=0.4cm$

To find:

$r_1$ and $r_2$ are radius of silver mold and cylindrical hole.

Volume of the silver on the elastic band$=?$

Solution:

Volume of the silver on the elastic band$=15($Volume of the silver mold$-$Volume of cylindrical hole$)$

$=15(\frac{4}{3}\pi r_1^3-\pi r_2^{2}h)$

$=15\left(\frac{4}{3}\pi \right(0.5{)}^3-\pi \times (0.2{)}^2\times 1)$

$=15(\frac{0.5\pi }{3}-0.04\pi )$

$=15\left(\frac{0.38\pi }{3}\right)$

$=\frac{19\pi }{10}c{m}^3$

Hence, C is the correct option.