The dimensions of Figure 2's base are determined by the ratio of heights and radii in the similar cylinders. Consequently, the circumference is 5π inches, and the area is 6.25π square inches.
Since the cylinders are similar, the ratio of corresponding dimensions in each cylinder remains constant. Specifically, the ratio of the radii of the cylinders is equivalent to the ratio of their heights.
Ratio of Radii:
r₂ / r₁ = h₂ / h₁
Ratio of Heights:
h₂ / h₁ = 5 / 9
Substituting to Find r₂:
r₂ = r₁ * (h₂ / h₁) = 4.5 in * (5 / 9) = 2.5 in
Circumference of the Base of Figure 2:
C₂ = 2πr₂ = 2π * 2.5 in = 5π inches
Area of the Base of Figure 2:
A₂ = πr₂² = π * (2.5 in)² = 6.25π square inches
Therefore, the completed statement is:
The circumference of the base of Figure 2 is 5π inches, and the area of the base of Figure 2 is 6.25π square inches.
Complete question:
Compete the statement about these similar cylinders. The circumference of the base of figure 2 is 9 π inches, and the area of the base of figure 2 20.25 π square inches (Hint: The circumference of a circle =2π r and the area of a circle =π r^2 , where r is the radius.)