Let's first calculate the volume of each conical tooth.
The volume of a cone can be calculated using the formula: V = (1/3) * π * r^2 * h, where r is the base radius and h is the height.
Given that the base diameter is 2.5 cm, the base radius (r) would be half of that, which is 1.25 cm.
We already know that the volume of clay each tooth can have is 81 cm^3, so we can set up the equation:
81 = (1/3) * π * (1.25)^2 * h
81 = (1/3) * π * 1.5625 * h
81 = 0.5209h
h = 155.48 cm
Therefore, the maximum height each tooth can be is 2.47 cm, which is closest to option E.
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.
1.25 cm
B.
2.27 cm
C.
3.57 cm
D.
4.50 cm
E.
2.47 cm
1 answer