A kaleidoscope is a tube-shaped instrument that contains mirror and colored glass. When a viewer looks in
one end, (s)he sees vibrant, changing patterns. Tami sees a kaleidoscope in the shape of triangular prism. It
has a height of 4 inches, a base of 5 inches and a depth of 8 inches. What is the volume in cubic inches of
the kaleidoscope?
v = Bh where B is the area of the base
Since the base is a triangle,
B = 1/2 * 4 * 5
Now, since h=8, you can easily see that v=80
To find the volume of the kaleidoscope, we need to use the formula for the volume of a triangular prism, which is given by:
Volume = (base area) x height
In this case, the base of the triangular prism is a triangle with a base of 5 inches and a height of 4 inches. The formula for the area of a triangle is given by:
Area = (base x height) / 2
So, we can calculate the base area of the triangular prism as:
Base area = (5 x 4) / 2
= 20 / 2
= 10 square inches
Now, we can find the volume of the kaleidoscope by multiplying the base area by the height:
Volume = Base area x Height
= 10 square inches x 8 inches
= 80 cubic inches
Therefore, the volume of the kaleidoscope is 80 cubic inches.