The volume of figure B is calculated to be 678.58 cubic feet.
Step-by-step explanation:
Step 1; The volume of a cone is determined by multiplying [tex]\frac{1}{3}[/tex] with π , square of the radius (r²) and height (h).
The volume of figure A = 25.12 = π × 2 × 2 × h / 3.
h = 25.12 × 3 / π × 4, h = 5.9969, so h for figure 1 equals 6 feet.
Step 2; As figures A and B are similar, their dimensions will be of the same ratio. The ratio of the radii of figure A to B will be the same as the ratio of heights of figure A to B. Assume the height of figure B is x.
[tex]\frac{radiusoffigureA}{radius of figureB}[/tex] = [tex]\frac{heightoffigureA}{heightoffigureB}[/tex], [tex]\frac{2}{6}[/tex] = [tex]\frac{6}{x}[/tex], x =[tex]\frac{6}{2}[/tex] × 6 = 18 feet.
The volume of figure B = π × 6 × 6 × 18 / 3 = 678.5840 cubic feet. By rounding this off, we get area equals 678.58 cubic feet.
