The vertices of a triangular underwater search region are shown in the graph. Each unit represents 1 kilometer.
Let the horizontal side be the base. The base is _ kilometers and the height is _
kilometers.
Answers
Answer:
Step-by-step explanation:
Here is a picture (graph) of the base (in blue) with a thin slice taken perpendicular to the
y
-axis (in black).
enter image source here
The thinkness of this representative slice is
d
y
so we need the sides of the square to be expressed in terms of
y
(not
x
).
The line on the right contains
(
0
,
0
)
and
(
4
,
4
)
. Its equation is
y
=
x
or
x
=
y
The line on the left contains
(
0
,
0
)
and
(
−
8
,
4
)
. Its equation is
y
=
−
1
2
x
or
x
=
−
2
y
The side of the square built on the representative slice is
s
=
x
greater
−
x
lesser
=
x
on the right
−
x
on the left
.
So,
s
=
y
−
(
−
2
y
)
=
3
y
.
The volume of the representative slice is
s
2
⋅
thickness
=
(
3
y
)
2
d
y
.
The values of
y
vary from
0
to
4
, so the volume of the solid is
V
=
∫
4
0
(
3
y
)
2
d
y
=
3
y
3
]
4
0
=
192
(cubic units)
