CPM Homework Help : GC Problem 9-49

Elliot has a modern fish tank that is in the shape of an oblique prism, shown at right. If the slant of the prism makes a $60°$ angle, find the volume of water the tank can hold. Assume all measurements are in inches.

Hint:

Use a special right triangle to find the height of the parallelogram.
For help, see the Math Notes box in Lesson 5.3.1.

Step 1:

Find the height of the parallelogram:

linear scale factor $= 6$

$h=6(1\sqrt{3})=6\sqrt{3}\approx 10.39 \text{ inches}$

Step 2:

Find the area of the base:

$\text{Area of parallelogram = area of prism base}$
$\text{Area of a parallelogram} = (\text{base})(\text{height})$
$= \left(13\right)\left(7\right)$
$= 91 \text{ inches}^2$

Step 3:

Find the volume of the prism:

$\text{Volume of prism} = (\text{area of base})(\text{depth})$
$≈ (91 \text{ inches}^2)(10.39 \text{ inches})$
$≈ 945.49 \text{ inches}^3$