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High School
Geometry
High school geometry
Finding volume
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Recent questions in Finding volume
High school geometry
Answered question
klepnin4wv
2022-12-17
The mean of sample A is significantly different than the mean of sample B. Sample A:
59
,
30
,
74
,
62
,
87
,
73
Sample B:
53
,
67
,
85
,
57
,
93
,
79
Use a two-tailed
t
-test of independent samples for the above hypothesis and data. What is the
p
-value? (Answer to
3
decimal places)
High school geometry
Answered question
Alberanteb4T
2022-12-04
Winton wants to find the volume of a cube. He uses the formula for volume of a cube V=s^(3), where s is the length of one side of the culbe. If s=0.5 centimeter, what is the volume of the cube? 0.125 cubic centimeter 0.25 cubic centimeter
High school geometry
Answered question
blogmarxisteFAu
2022-12-01
A sample of an ideal gas has a volume of 3.70 L at 11.40 °C and 1.50 atm. What is the volume of the gas at 22.80 °C and 0.988 atm
High school geometry
Answered question
Tristin Wu
2022-11-28
Determine if the graph is symmetric about the
x
-
axis, the
y
-
axis, or the origin.
r
=
2
cos
5
θ
?
High school geometry
Answered question
Gharib4Pe
2022-11-25
Сalculate what is the volume of a box with a width of
1
1
2
inches, a length of
2
1
2
inches, and a height of
4
inches?
High school geometry
Answered question
Kyler Oconnor
2022-11-20
Finding the volume below the part of the plane which is above the xy-plane
My function is
f
(
x
,
y
)
=
2
−
|
x
|
−
|
y
|
and I'm supposed to find the volume below the part of the plane which is above the xy-plane.
I don't understand how to find the limits of my integrals for this problem. I have tried to draw the lines for all the cases for which the absolute value of x and y is both positive and negative, but I don't see the limits. Is there anyone who has any suggestions?
High school geometry
Answered question
Aron Heath
2022-11-19
Finding volume of a washer via integration
Objective: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.
y
=
x
2
,
x
=
y
2
; rotated about
y
=
1
.
I know how to sketch the graph. I assumed the integral would be:
π
∫
0
1
[
(
x
2
)
2
−
(
x
)
2
]
d
x
I checked the solution and it's actually:
π
∫
0
1
[
(
1
−
x
2
)
2
−
(
1
−
x
)
2
]
d
x
I know this must have something to do with the rotation about
y
=
1
but that's it. Would the integral be:
π
∫
0
1
[
(
1
+
x
2
)
2
−
(
1
+
x
)
2
]
d
x
if I were to rotate it by
y
=
−
1
? All answers will be appreciated.
High school geometry
Answered question
mxty42ued
2022-11-17
Finding the bounds to solve for the volume using cylindrical coordinates
My goal is to set up the triple integral that will solve for the volume inside the sphere
x
2
+
y
2
+
z
2
=
2
z
and above the paraboloid
x
2
+
y
2
=
z
using cylindrical coordinates.
Upon solving, I know that the intersection of the sphere and the paraboloid is
r
=
1
and the bounds for
θ
is
0
≤
θ
≤
2
π
.
However, I am uncertain for the bounds of the z variable. I solve for the value of z in converted equation of the sphere
r
2
+
z
2
=
2
z
. By quadratic formula, I got the value of
z
=
2
±
4
−
4
r
2
2
.
Should I only include
z
=
1
2
(
2
+
4
−
4
r
2
)
as one of the bounds in the z variable? Or there will be a split integral? My yielding triple integral in this case if I only include
z
=
1
2
(
2
+
4
−
4
r
2
)
would be
∫
0
2
π
∫
0
1
∫
r
2
1
2
(
2
+
4
−
4
r
2
)
r
d
z
d
r
d
θ
High school geometry
Answered question
Howard Nelson
2022-11-12
Using Symmetry for finding volume
I have a confusion regarding the symmetry of the volume in the following question.
Find the volume common to the sphere
x
2
+
y
2
+
z
2
=
16
and cylinder
x
2
+
y
2
=
4
y
.
The author used polar coordinates
x
=
r
c
o
s
θ
and
y
=
r
s
i
n
θ
and does something like this:
Required volume
V
=
4
∫
0
π
/
2
∫
0
4
s
i
n
θ
(
16
−
r
2
)
1
/
2
r
d
r
d
θ
. The reason for multiplying by 4 is the symmetry of the solid w.r.t. xy-plane.
My point of confusion is that this solid cannot be cut into 4 identical parts, so how it can be multiplied by 4?
High school geometry
Answered question
gfresh86iop
2022-11-12
A "significant" solid with volume
3
3
π
r
3
?
In a painting:
there is this formula of volume:
V
=
3
3
π
r
3
It seems to me this is the formula of the volume of some polyhedron inscribed or circumscribed to a sphere of radius r, but I am not expert of the field.
I had the task of finding the meaning of the different formulas, that were taken from a web site whose address has been lost, so I need to find the regular solid that corresponds to such formula, if it exists.
So I am asking help from somebody more expert then me in the field of geometry of solids, if there is some "significant" solid with the volume given by that formula.
High school geometry
Answered question
Rigoberto Drake
2022-11-12
Finding Volume of the Solid-washer method
The region between the graphs of
y
=
x
2
and
y
=
3
x
is rotated around the line
x
=
3
.
What is the volume of the resulting solid?
I drew the picture, and I saw that I should be using the washer method. Since the region was being flipped at
x
=
3
, I would have to make sure I am subtracting the two functions from 3 and then subtract those two, but I could not seem to get the right answer.
High school geometry
Answered question
Nico Patterson
2022-11-11
Finding Volume of Cube from Co-Ordinate Points
If I am given two 3-D points of a cube,how do I find the volume of that Cube? where
(
x
1
,
y
1
,
z
1
)
is the co-ordinate of one corner and
(
x
2
,
y
2
,
z
2
)
is the co-ordinate of the opposite corner.
High school geometry
Answered question
figoveck38
2022-11-10
Understanding shell height (finding volume)
- Use cylindrical shells to find the volume of the solid obtained by rotating about the x-axis the region under curve
y
=
x
from 0 to 1.
Shell radius
=
y
Shell height
=
1
−
y
2
V
=
2
π
∫
0
1
y
(
1
−
y
2
)
d
y
I didn't understand the shell height, why it is
1
−
y
2
? Why not
y
2
? I think, shell height should be
y
2
. Can you explain?
High school geometry
Answered question
Rosemary Chase
2022-11-10
The volume of the region between two spheres and the upper nappe of a cone
I am really having trouble constraining the region between these three surfaces. I am imagining a sort of "Dome", or a "muffin head" sort of shape. Is this correct ? Anyway, I need to be able to write the following volume integral in rectangular, cylindrical and spherical coordinates:
Consider the region that is between
x
2
+
y
2
+
z
2
=
1
,
x
2
+
y
2
+
z
2
=
9
, and finally above the upper nappe of the cone
z
2
=
3
(
x
2
+
y
2
)
.
Upon further consideration, does the smaller sphere even matter?
High school geometry
Answered question
Messiah Sutton
2022-11-09
Volume by disk perpendicular to x axis
Find the volume of the solid formed when region enclosed by
y
=
x
1
/
2
,
y
=
6
−
x
,
y
=
x
1
/
2
,
y
=
6
−
x
and
y
=
0
revolves around x axis.
Can I use the equation for finding solids by splitting the solid into 2 parts?
High school geometry
Answered question
assupecoitteem81
2022-11-08
Finding the volume of a solid by rotating two curves about the y-axis
y
=
56
x
−
7
x
2
and
y
=
0
My issue with this question is that I am having trouble turning the equation,
y
=
56
x
−
7
x
2
, in terms of y. I understand that by doing that, I can proceed with the integration... Perhaps there is another method to do this without having to turn it in terms of y?
High school geometry
Answered question
Owen Mathis
2022-11-05
Volume of the solid
Using geometry, calculate the volume of the solid under
z
=
49
−
x
2
−
y
2
and over the circular disk
x
2
+
y
2
≤
49
.
I am really confused for finding the limits of integration. Any help?
High school geometry
Answered question
Jenny Roberson
2022-11-04
Finding two sides of a cuboid while knowing the volume
The volume of a cuboid is
150
m
3
, one side is 2,5m, one side is completely unknown (x) and the other one is 4 meters longer
x
+
4
. guessed the sides one being 6 and the other 10 but I need to figure it out with a formula.
High school geometry
Answered question
Jonas Huff
2022-11-03
Check my work? Finding line that divides rotational volume into equal parts. Not getting right answer.
I need to rotate the area between the curve
y
=
x
2
and
y
=
9
, bounded in the first quadrant, around the vertical line
x
=
3
. I then must find the height (m) of the horizontal line that divides the resulting volume in half.
I've been trying to set up two integrals with washers. One from
∫
m
9
3
2
−
(
3
−
x
)
2
d
y
and the other for the bottom region
∫
0
m
3
2
−
(
3
−
x
)
2
d
y
. The 3 is the outer radius of the washer and the
3
−
x
gives the inner hole of the washer. I can't seem to get the right answer.
π
∫
m
9
(
6
y
−
y
)
d
y
=
π
(
4
y
3
2
−
1
2
y
2
)
evaluated from 9 to m
=
π
(
135
2
−
(
4
m
3
2
−
1
2
m
2
)
. Similarly, for the bottom region integral, I get
π
(
4
m
3
2
−
1
2
m
2
)
. I then try to set the volumes equal to each other and solve for m.
I believe the answer I should get is
9
2
3
but I don't get that value for m.
If I continue, I get
135
2
=
8
m
3
2
-
m
2
but I don't see any easy way to solve without using a calculator.
High school geometry
Answered question
Barrett Osborn
2022-11-02
Find volume under given contraints on the Cartesian plane.
The constrains are given as
x
2
+
y
2
+
z
2
⩽
64
,
x
2
+
y
2
⩽
16
,
x
2
+
y
2
⩽
z
2
,
z
⩾
0
.
With the goal of finding the Volume. Personally, I have trouble interpreting the constrains in terms of integrals to find the Volume. However, logically z can be maximum of 8 and x or y no larger than 4.
1
2
3
4
5
…
12
Finding the volume of an object is a simple but important math skill. Whether you need to measure the capacity of a container or the size of a solid, knowing how to calculate the volume of certain shapes can help you solve many everyday tasks. Our site offers easy-to-follow tutorials on how to find the volume of different shapes, like cubes, cylinders, and cones. We also have a library of formulas and tools to help you determine the exact volume of any object. Start exploring today and learn how to find the volume of different shapes in no time!
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