Question

Can someone help with this question?

Answer 1

You solve an expression for a variable if that variable sits alone on one side of the equation, and everything else is on the other side.

So, our goal is to leave $h$ alone on the right hand side, and move everything else to the left.

So, we start with

$V = \dfrac{1}{3}s^2h$

We multiply both sides by 3:

$3V = s^2h$

We divide both sides by $s^2$

$\dfrac{3V}{s^2} = h$

To compute the required height, simply plug in the values:

$\dfrac{3\cdot 400}{10^2} = \dfrac{3\cdot 400}{100} = 3\cdot 4 = 12$

Answer 2

Answer: $\bold{h=\dfrac{3V}{s^2}, \qquad h=12}$

Step-by-step explanation:

Isolate the variable "h" by multiplying both sides by 3 and dividing both sides by s².

$V=\dfrac{1}{3}s^2h$

$(3)V=(3)\dfrac{1}{3}s^2h\ \quad \rightarrow\ \quad 3V=s^2h$

$\dfrac{3V}{s^2}=\dfrac{s^2h}{s^2}\ \quad \rightarrow \quad \dfrac{3V}{s^2}=h$

Next, substitute V = 400 and s = 10 to solve for h:

$h=\dfrac{3(400)}{(10)^2}$

   $=\dfrac{1200}{100}$

   $= 12$