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

To solve this problem, we first need to find the volume of one conical shark tooth. The formula for the volume of a cone is given by: \[ V = \frac{1}{3} \pi r^2 h \] Here, \( r \) is the radius, and \( h \) is the height of the cone. Given that the base diameter is 2.5 cm, the radius \( r \) is \( \frac{2.5}{2} = 1.25 \) cm. Now, there are 20 conical teeth, which means the total volume of all teeth will be: \[ V_{total} = 81 \text{ cm}^3 \] Now, for one tooth: \[ V_{one\ tooth} = \frac{V_{total}}{20} = \frac{81}{20} = 4.05 \text{ cm}^3 \] Substituting the values into the volume formula: \[ 4.05 = \frac{1}{3} \pi (1.25)^2 h \] Calculating \( (1.25)^2 \): \[ (1.25)^2 = 1.5625 \] Substituting back: \[ 4.05 = \frac{1}{3} \pi (1.5625) h \] Solving for \( h \): \[ h = \frac{4.05 \cdot 3}{\pi \cdot 1.5625} \] Calculating the right side gives: \[ h \approx \frac{12.15}{4.9087} \approx 2.47 \text{ cm} \] So, the answer is B. \( \quad 2.47 \mathrm{~cm} \)