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.
1.25 cm
2.27 cm
2.47 cm
3.57 cm
4.50 cm

Question

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.
1.25 cm
2.27 cm
2.47 cm
3.57 cm
4.50 cm

anonymous · Answer

V = ( π.r^2.h) /3 
The block has volume = 81cm ³ and total 20 teeth should be done. 
However, each tooth having a diameter of 2.5 cm which results in a radius of 1.25 cm 
soon if we use the formula of the volume of the cone will be possible to find the result, since multiply by 20 because that is the necessary condition of the exercise. "There should be 20 teeth" we find the height:

20.[(π.r².h)/3)] = 8
20.[(3,14.1,25².h)/3] =81
20[4,90h] = 243 
98h = 243
h = 243/98
h = 2,47 cm