Question

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 cm³ 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. 3.57 cm b. 2.27 cm c. 1.25 cm d. 4.50 cm e. 2.47 cm

Explanation:

Step1: Find volume of one tooth

$V_{tooth}=\frac{81}{20}=4.05$ $cm^{3}$

Step2: Find radius

$r = \frac{2.5}{2}=1.25$ $cm$

Step3: Use cone - volume formula

$V=\frac{1}{3}\pi r^{2}h$, so $h=\frac{3V}{\pi r^{2}}=\frac{3\times4.05}{\pi\times(1.25)^{2}}\approx2.47$ $cm$

Answer:

E. 2.47 cm