Answer:
It is given that the volume of a cone = cubic units
Volume of cone with radius 'r' and height 'h' =
Equating the given volumes, we get
×
It is given that the height is 'x' units.
Therefore,
Therefore,
So, the expression '' represents the radius of the cone's base in units.
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Explanation:
Check out the diagram below.
Plot R(-3,7) and T(3,-11) on the same xy grid.
Draw a vertical line through R and a horizontal line through T. A right triangle forms. At the intersection point is point S(-3,-11)
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Now measure the distance from point S to point T. You can count out the spaces or subtract the x coordinates and use absolute value.
|x1-x2| = |-3-3| = |-6| = 6
From point S to point T is 6 units.
We want to subdivide this horizontal length in the ratio 1:2
What this means is that we want to plot a point U somewhere such that SU:UT = 1:2
In other words,
SU = x
UT = 2x
SU+UT = ST
x+2x = 6
3x = 6
x = 6/3
x = 2
So we must move 2 spaces to the right from point S to get to U(-1,-11)
Going from point U(-1,-11) to T(3,-11) is 4 spaces
We have SU:UT = 2:4 = 1:2 to help confirm we have the correct location for point U
From point U, we then move straight up to the line segment RT
We'll land on Q(-1,1)
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Another way to find the y coordinate of point Q is to subdivide the segment RS into the ratio 1:2 similar to how we divided ST up
Segment RS is 18 units long since we go from y = 7 to y = -11 when going from R to S.
If V was on segment RS such that
RV:VS = 1:2
and RV = y
then
RV+VS = RS
y+2y = 18
3y = 18
y = 6
RV = y = 6
VS = 2y = 2*6 = 12
So you'll move 6 units down from y = 7 to land on y = 1 (when going from the y coordinate of R to the y coordinate of Q)
