Answer
$800ft^{3}$
Work Step by Step
Since the exercise says that the volume of a pyramid varies JOINTLY as its height and area of the base, we can express this in the following manner:
$$V_{pyramid} = khA_{base}$$
where $V$ is the volume of the pyramid, $h$ is the height of the pyramid, $A$ is the area of the base of the pyramid and $k$ is a proportionality constant. Since we know that, when $h=15$ and $A=35$, $V=175$, we can calculate $k$ as so:
$$V = khA$$
$$\frac{V}{hA} = k$$
$$\frac{(175)}{(15)(35)} = k = \frac{1}{3}$$
and, finally, we can answer the question:
$$V = \frac{1}{3}(20)(120)$$
$$V = 800$$
