Question

where can I get the volume of this u-shaped diagram?

Answer 1

Answer:

Recall that the volume of a shaped diagram is given by the following formula:

$\text{Volume}=BaseArea\times length\text{.}$

Now, to compute the area of the given base, we will divide the figure as follows:

Then the area of the given figure is:

$A=9\operatorname{cm}\times2\operatorname{cm}+6\operatorname{cm}\times2\operatorname{cm}+6\operatorname{cm}\times2\operatorname{cm}\text{.}$

Simplifying the above result we get:

$\begin{gathered} A=18cm^2+12cm^2+12cm^2, \\ A=42cm^2\text{.} \end{gathered}$

Therefore the volume of the given u-shaped diagram is:

$V=42cm^2\cdot7\frac{1}{2}cm=42cm^2\cdot7.5\operatorname{cm}.$

Simplifying the above result we get:

$V=315cm^3\text{.}$

The volume of the given diagram is 325 cubic centimeters.