Final answer:
The value of k in the expression 'k(pi) cm³' for the total volume of the shape is 51.
Step-by-step explanation:
The volume of the cone can be calculated using the formula:
Vcone = (1/3)×π×r²×h
Given that the height of the cone is 11cm and the base of the cone has a diameter of 6cm, the radius of the cone's base is half of the diameter, which is 3cm. Substituting these values into the formula gives:
Vcone = (1/3)×π×3cm²×11cm = 33×π cm³
The volume of the hemisphere can be calculated using the formula:
Vhemisphere = (2/3)×π×r³
Given that the diameter of the hemisphere is 6cm, the radius is half of the diameter, which is 3cm. Substituting this value into the formula gives:
Vhemisphere = (2/3)×π×3cm³ = 18×π cm³
The total volume of the shape is the sum of the volume of the cone and the volume of the hemisphere:
Vtotal = Vcone + Vhemisphere = 33×π + 18×π = 51×π cm³
Therefore, the value of k in the expression 'k×π cm³' is 51.