Answer:
1023.9 ft^3
Explanation:
The below formula can be used to find the volume of a cone;
[tex]V=\pi\times r^2\times\frac{h}{3}[/tex]where r = radius of the base
h = height of the cone
Given the radius of cone A as 18 inches(18/12 = 1.5 ft) and the volume of cone A as 54 ft^3, we can go ahead and solve for the height of cone A;
[tex]\begin{gathered} 54=3.14\times(1.5)^2\times\frac{h_A}{3} \\ h_A=\frac{162}{7.065} \\ h_A=22.93ft \end{gathered}[/tex]We're told that cone A and B are similar, therefore the ratios of the radii and heights must be the same;
[tex]\begin{gathered} \frac{h_B}{h_A}=\frac{48}{18} \\ h_B=\frac{22.93\times48}{18} \\ h_B=61.14ft \end{gathered}[/tex]Since we now know that the height of cone B to be 61.14ft and we're given the radius of cone B to 48 inches (48/12 = 4ft), we can go ahead and determine the volume of cone B as shown below;
[tex]\begin{gathered} V_B=3.14\times(4)^2\times\frac{61.14}{3} \\ V_B=1023.9ft^3 \end{gathered}[/tex]