Next Unit Posttest Submit Test Reader Tools 8 Select the correct answer. Tim is an elementary school art teacher. His students are sculpting a replica of a shark out of clay. Tim has given them one block of clay to make 20 conical shark teeth for the sculpture. The block contains $$ 81 \mathrm{~cm}^{3} $$ of clay. If each tooth is solid and has a 2.5 cm base diameter, what is the maximum height each tooth can be? Assume that the students use all the clay. A. $$ \quad 1.25 \mathrm{~cm} $$ B. $$ \quad 2.47 \mathrm{~cm} $$ C. $$ \quad 4.50 \mathrm{~cm} $$ D. $$ \quad 2.27 \mathrm{~cm} $$ E. $$ \quad 3.57 \mathrm{~cm} $$ Reset Next

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To determine the maximum height each conical shark tooth can be, we can follow these steps:

1. **Calculate the Volume Available per Tooth:**
   - Total volume of clay = $$ 81 \, \text{cm}^3 $$
   - Number of teeth = 20
   - Volume per tooth = $$ \frac{81 \, \text{cm}^3}{20} = 4.05 \, \text{cm}^3 $$

2. **Use the Volume Formula for a Cone:**
   $$
   V = \frac{1}{3} \pi r^2 h
   $$
   Where:
   - $$ V $$ is the volume
   - $$ r $$ is the radius of the base
   - $$ h $$ is the height

3. **Plug in the Known Values:**
   - Diameter of the base = 2.5 cm, so radius $$ r = \frac{2.5}{2} = 1.25 \, \text{cm} $$
   - Volume per tooth $$ V = 4.05 \, \text{cm}^3 $$

$$
   4.05 = \frac{1}{3} \pi (1.25)^2 h
   $$

4. **Solve for Height $$ h $$:**
   $$
   h = \frac{4.05 \times 3}{\pi \times (1.25)^2} = \frac{12.15}{\pi \times 1.5625} \approx \frac{12.15}{4.9087} \approx 2.47 \, \text{cm}
   $$

**Answer:**  
**B. $$ \quad 2.47 \mathrm{~cm} $$**
Each conical shark tooth can be up to approximately $$ 2.47 \, \text{cm} $$ tall.

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