Answer:
First blank = [tex]\pi r^{2}[/tex]
Second blank = [tex]\frac{1}{3}[/tex]
Third blank = [tex]\frac{1}{3} \pi r^{2} h[/tex]
Step-by-step explanation:
We are given,
The argument to explain the derivation of the formula for the volume of a cone.
According to the explanation, we have,
First blank: It represents the area of the base of the cylinder.
Since, the base of the cylinder is a circle.
And, area of the circle = [tex]\pi r^{2}[/tex]
Thus, the first blank = [tex]\pi r^{2}[/tex]
Second blank: It represents the number by which volume of the cylinder is multiplied to obtain the volume of the cone.
Since, we know,
[tex]\frac{1}{3}[/tex] of Volume of cylinder is given by volume of the cone.
Hence, the second blank = [tex]\frac{1}{3}[/tex]
Third blank: It represents the formula for the volume of the cone.
As, Volume of the cone = [tex]\frac{1}{3} \pi r^{2} h[/tex]
Thus, third blank = [tex]\frac{1}{3} \pi r^{2} h[/tex]
