Question

Multiple choice a. 12 pie cm b. 21 pie cm c. 35 pie cm

Answer 1

Answer:

The correct option is;

a. 12 pie cm

Step-by-step explanation:

Cavalieri's principle states that if the cross-sectional area of two or more figures of the same altitude are the same at each level of the figures, then the volumes of the figures are also the same;

Given that the base area of the square based prism and the cylinder are the same, and that the square based prism and the cylinder have equal height of 4 cm, then by Cavalieri's principle, their volumes are the same

The volume of the square based prism = 452 cm³

Therefore, the volume of the cylinder (of equal base area) = 452 cm³

The formula for the volume of square based prism = Area of base × Height

∴ The volume of square based prism, 452 cm³ = Area of base × 4 cm

Which gives;

Area of the base of the square based prism  = 452/4 = 113 cm²

The area of the base of the cylinder $A_c$  = The area of the base of the square based prism = 113 cm²

The area of the base of the cylinder,$A_c$  is given by the following equation;

$A_c$ = π×r² = 113 cm²

r = √(113/π) = √35.97 ≈ √36  = 6 cm

The circumference of the base of the cylinder,$C_c$  is given by the following equation

$C_c$ = 2×π×r ≈ 2×π×6 = 12×π cm

The correct option is 12 pie cm.