A cereal box has a length of 9 inches, a width of 3 inches, and a height of 13 inches. What is the volume of the cereal box?
2 answers:
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Answer:
1 and 2.
Midpoints calculated, plotted and connected to make the triangle DEF, see the attached.
- D= (-2, 2), E = (-1, -2), F = (-4, -1)
3.
As per definition, midsegment is parallel to a side.
Parallel lines have same slope.
<u>Find slopes of FD and CB and compare. </u>
- m(FD) = (2 - (-1))/(-2 -(-4)) = 3/2
- m(CB) = (1 - (-5))/(1 - (-3)) = 6/4 = 3/2
- As we see the slopes are same
<u>Find the slopes of FE and AB and compare.</u>
- m(FE) = (-2 - (- 1))/(-1 - (-4)) = -1/3
- m(AB) = (1 - 3)/(1 - (-5)) = -2/6 = -1/3
- Slopes are same
<u>Find the slopes of DE and AC and compare.</u>
- m(DE) = (-2 - 2)/(-1 - (-2)) = -4/1 = -4
- m(AC) = (-5 - 3)/(-3 - (-5)) = -8/2 = -4
- Slopes are same
4.
As per definition, midsegment is half the parallel side.
<u>We'll show that FD = 1/2CB</u>
- FD =
=
=
- CB =
=
= 2
- As we see FD = 1/2CB
<u>FE = 1/2AB</u>
- FE =
=
=
- AB =
=
= 2
- As we see FE = 1/2AB
<u>DE = 1/2AC</u>
- DE =
=
=
- AC =
=
= 2
- As we see DE = 1/2AC
The space is inside the cylinder but outside the cone is 200π cubic FT or 628.32 cubic FT.
<h3>What is a cone?</h3>It is defined as the three-dimensional shape in which the base is a circular shape and if we go from circular base to top the diameter of the circle reduces and at the vertex, it becomes almost zero.
We know the volume of the cylinder is given:
r = 10/2 = 5 FT
h = 12 FT
V = 300π cubic FT
Volume of the cone:
v = 100π cubic FT
Space is inside the cylinder but outside the cone = 300π - 100π
= 200π cubic FT
= 628.32 cubic FT
Thus, the space is inside the cylinder but outside the cone is 200π cubic FT or 628.32 cubic FT.
Learn more about the cone here:
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