The volume V of a pyramid varies jointly as the area of the 1. ________________________
base B and the height h, and V=24 ft3
when B=12 ft2 and h=6ft.
Find B when V=54 ft3
and h=9 ft.
To find the value of B when V=54 ft^3 and h=9 ft, we need to use the given information that the volume V of a pyramid varies jointly as the area of the base B and the height h.
Let's set up the equation using the given values for V, B, and h:
V = k * B * h
where k is the constant of variation.
We can solve for k by substituting the given values of V, B, and h when they were equal to 24 ft^3, 12 ft^2, and 6 ft, respectively:
24 = k * 12 * 6
24 = 72k
k = 24/72
k = 1/3
Now that we have the value of k, we can substitute it into the equation and solve for B:
54 = (1/3) * B * 9
54 = 3B
B = 54/3
B = 18 ft^2
Therefore, when V = 54 ft^3 and h = 9 ft, the value of B is 18 ft^2.