Question

Cone A has a radius 18 inches and Cone B has a radius of 48inches. If the cones are similar and the volume of Cone A is 54 ft^3,find the volume of Cone B.

Answer 1

1023.9 ft^3

Step-by-step explanation:

The below formula can be used to find the volume of a cone;

`V=\pi* r^2*(h)/(3)`

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;

`\begin{gathered} 54=3.14*(1.5)^2*(h_A)/(3) \\ h_A=(162)/(7.065) \\ h_A=22.93ft \end{gathered}`

We're told that cone A and B are similar, therefore the ratios of the radii and heights must be the same;

`\begin{gathered} (h_B)/(h_A)=(48)/(18) \\ h_B=(22.93*48)/(18) \\ h_B=61.14ft \end{gathered}`

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;

`\begin{gathered} V_B=3.14*(4)^2*(61.14)/(3) \\ V_B=1023.9ft^3 \end{gathered}`