Answer
$800$ cubic feet.
Work Step by Step
Step 1:- Translate the statement to form an equation.
Let the volume of a pyramid be $V$,
the height be $H$,
and the area of its base be $A$.
Because $V$ varies jointly as $H$ and $A$, we have:
$\Rightarrow V=kHA$ ...... (1)
Step 2:- Substitute the first set of values into the equation to find the value of $k$.
The given values are $H=15$ feet ,$A=35$ square feet and $V=175$ cubic feet.
Substitute into the equation (1).
$\Rightarrow 175=k(15)(35)$
Simplify.
$\Rightarrow 175=525k$
Divide both sides by $525$.
$\Rightarrow \frac{175}{525}=\frac{525k}{525}$
Simplify.
$\Rightarrow \frac{1}{3}=k$
Step 3:- Substitute the value of $k$ into the original equation.
Substitute $k=\frac{1}{3}$ into the equation (1).
$\Rightarrow V=\frac{1}{3}HA$ ...... (2)
Step 4:- Solve the equation to find the required value.
Substitute $H=20$ feet and $A=120$ square feet into the equation (2).
$\Rightarrow V=\frac{1}{3}(20)(120)$
Simplify.
$\Rightarrow V=800$
Hence, the volume of a pyramid is $800$ cubic feet.
