Hillassg24

course Mth 152

d?t??????????assignment #024024. `query 24

Liberal Arts Mathematics II

11-24-2008

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20:02:10

**** query 9.5.12 vol of sphere diam 14.8 **** What is the volume of the sphere and how did you obtain it?

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RESPONSE -->

The formula for finding the volume of a sphere is

4/3 x 3.14 x r^3

The radius is half of the diameter so it would be 7.4

Volume = 4/3 x 3.14 x 7.4^3

4/3 x 3.14 x 405.224

Volume = 1692.29

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20:02:53

I use the formula for finding the volume of a sphere which is 4/3(3.14)(r^3).

Since the diameter is 14.8, the radius is half that which is 7.4.

V = 4/3 * 3.14 * 7.4^3

V = 4/3 * 3.14 * 405.224

V = 1696.54

The volume is 1696.54

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RESPONSE -->

O.k.

How did you come up with the answer 1696.54?

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20:07:59

**** query 9.5.18 pyramid 12 x 4 altitude 10 **** What is the volume of the pyramid and how did you find it?

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RESPONSE -->

The formula for finding the volume of a pyramid is 1/3Bh

12 x 4 = 48 (base)

1/3 x 48 x 10

1/3 x 480

volume = 160

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20:08:06

I used the formula : V = 1/3Bh

The base = 12 * 4 = 48

V = 1/3 * 48 * 10

V = 1/3 * 480

V = 160

The volume is 160ft.^3

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RESPONSE -->

o.k.

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20:13:54

**** query 9.5.24 bottle 3 cm alt 4.3 cm **** What is the volume of the bottle and how did you find it?

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RESPONSE -->

the bottle would be in the shape of a right circular cylinder

Volume = pi x r^2 x h

diameter is 3 so the radius is 1.5

3.14 x 1.5^2 x 4.3

3.14 x 2.25 x 4.3

Volume = 30.3795

30.38

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20:13:59

** The figure is a right circular cylinder with V = 3.14 * r^2 * h

Since the diameter is 3, then the radius is 1.5

V = 3.14 * 1.5^2 * 4.3

V = 3.14 * 2.25 * 4.3

V = 30.38 cm^3 **

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RESPONSE -->

o.k.

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20:28:16

**** query 9.5.36 sphere area 144 `pi^2 **** What are the radius, diameter and volume of the sphere and how did you find them?

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RESPONSE -->

Volume and surface area of a sphere

V = 4/3 pi r^3 S=4pir^2

4 pi r^2 = 144 pi m^2

I have to divide each side by 4 because (4pi)

r^2 = 36 m^2

r = 6 if the radius is 6 then the diameter is 2 x 6

diameter = 12

Volume= 4/3 x 3.14 x 6m^3 =150.12

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20:30:07

** Sphere area is 4 pi r^2, so we have

4 pi r^2 = 144 pi m^2. Dividing by 4 pi we get

r^2 = 36 m^2. Taking the square root of both sides we get

r = 6 m.

From this we find that the diameter is 2 * 6 m = 12 m and the volume is 4/3 pi * (6 m)^2 = 48 pi m^2. **

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RESPONSE -->

I thought that the formula for volume was

4/3 pi r ^3

144 pi^2 is the area of the sphere, not the volume. So you would have to use the area formula.

Nevertheless, he did a good job with the volume formula.

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20:36:37

**** query 9.5.48 cone alt 15 rad x vol 245 `pi **** What is the value of x and how did you find your result?

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RESPONSE -->

the formula for the volume of a cone is

1/3 3.14 x r^2 xh

I am lost on this one

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20:37:10

** We have V = 1/3 pi r^2 h. To solve for r we multiply both sides by 3 / (pi * h) to get

3 V / (pi * h) = r^2 then take the square root to get

r = sqrt(3 V / ( pi * h). Substituting we get

r = sqrt( 3 * 245 / (3.14 * 15) ) = 3.9 approx. **

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RESPONSE -->

o.k

will have to work on this one

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20:37:47

**** query 9.5.51 plane intersects sphere passing 7 in from center forming circle with area 576 `pi **** What is the volume of the sphere and how did you obtain it?

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RESPONSE -->

Can't do

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20:38:19

** The circle does have radius sqrt(576 in^2) = 24 in. However that is not the radius of the sphere since the plane containing the circle passes 7 in from the center of the sphere. So the center of the circle is not the center of the sphere.

The center of the circle is 7 in from the center of the sphere. Note also that a line from the center of the sphere to the center of the circle will be perpendicular to the plane of the circle.

Thus if you start at the center of the sphere and move the 7 in straight to the center of the circle, then move the 24 in to the rim of the circle, then back to the center of the sphere you will have traced out a right triangle with legs 7 in and 24 in. The hypotenuse of the triangle is the radius R of the sphere.

So we have

R^2 = 7^2 + 24^2 = 625 and

R = 25.

The radius of the sphere is 25 in. **

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RESPONSE -->

I don't seem to understand this one but will work on it.

This is a tough problem, harder than anything you are likely to see on the test. Don't worry too much about it, but of course if you can get it you will be prepared for about anything you might encounter on the test.

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20:39:05

**** Query Add comments on any surprises or insights you experienced as a result of this assignment.

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RESPONSE -->

The last two problems were very hard and I'll work on trying to solve them.

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20:39:17

I don't think that my last answer is correct. Also, in the first problem, the answer should be 1696.54 cm^3, instead of just 1696.54

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RESPONSE -->

o.k.

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&#Your work looks good. See my notes. Let me know if you have any questions. &#