M/ 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
Св.
2.27 cm
c.
2.47 cm
D
3.57 cm
E. 4.50 cm

Explanation:

We have 81 cm^3 of clay. Divide this among the 20 students and each gets 81/20 = 4.05 cm^3 of clay

The volume of a cone is

V = (1/3)*pi*r^2*h

Solving for h gets us

3V = pi*r^2*h

(3V)/(pi*r^2) = h

h = (3V)/(pi*r^2)

The diameter is 2.5 cm which cuts in half to 1.25 cm, so this is the radius.

We'll plug this radius in, along with V = 4.05 and pi = 3.14

h = (3V)/(pi*r^2)

h = (3*4.05)/(3.14*(1.25)^2)

h = 2.4764

This value is approximate. Rounding down to the nearest hundredth gets us 2.47

We round down because rounding up to 2.48 will lead to a volume larger than 4.05