Math Is Fun Forum

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi Relentless and bobbym,

The solution M#160 is correct! Excellent!

M#161. A lead pencil is the the shape of a right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm, find the volume of the wood used in the pencil.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mensuration

Hi;

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi bobbym and Relentless,

The solution M#161 is correct! Neat work!

M#162. Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mensuration

Hi;

I worked out a formula for this information:

V = 1/3 * pi * √(L^2 * r^4 - r^6)

Last edited by Relentless (2015-12-28 03:01:56)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi Relentless and bobbym,

The solution M#162 is correct! Neat work!

M#163. The radius and height of a right circular cone are in the ratio 2:3. Find the slant height if its volume is 100.48 cubic centimeters.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mensuration

Hello;
The exact answers for slant height, height and radius are a bit complicated, even with the 22/7 ~ pi approximation. However, to ten significant figures, the answers I get are:

Last edited by Relentless (2015-12-28 19:16:07)

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi bobbym and Relentless,

Excellent, bobbym!

M#164. Find the mass of 200 steel spherical ball bearings, each of which has radius 0.7 cm, given that the density of steel is 7.95 grams per cubic centimeters.
Mass = Volume x Density

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mensuration

Oh I see, I must have misapplied something. Interestingly, however, it seems that using 3.14 ~ pi gets you an answer of about 7.211102551cm, while using the exact value gives about 7.744657513cm. The discrepancy is either because of the compounding squaring and square-rooting going on, or because I am again wrong xD

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi Relentless and bobbym,

(1) Relentless - M#164 is unanswered. Please post the solution, for M164 and M#165.
(2) bobbym:

The solution M#164 is correct! Excellent, bobbym!

M#165. A cuboid shaped slab of iron whose dimensions are 55 cm x 40 cm x 15 cm is melted and recast into a pipe. The outer diameter and thickness of the pipe are 8 cm and 1 cm respectively. Find the length of the pipe.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi bobbym,

The solution M#165 is perfect! Excellent!

M#166. A play-top is in the form of a hemisphere surmounted on a cone. The diameter of the hemisphere is 3.6 cm. The height of the play-top is 4.2 cm. Find the total surface area.
Solution in terms of

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi bobbym,

The solution M#166 is correct! Remarkable!

M#167. A solid is in the shape of a cylinder surmounted on a hemisphere. If the diameter and the height of the solid are 21 cm and  25.5 cm respectively, then find its volume.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi bobbym,

The solution  M#167 is correct! Excellent!

M#168. A rent is in the shape of a right circular cylinder surmounted by a cone. The total height and the diameter of the base are 13.5 m and 28 m. If the height of the cylindrical portion is 3 m, find the total surface area of the tent.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mensuration

Hello!
I think diagrams would be helpful for most of these xD They turn into interpretation problems just as much as geometry problems.
I assume that we want the curved surface area of the cone, plus the open surface area of the cylinder (i.e. without the top), where the radius is in common.

Last edited by Relentless (2015-12-30 19:18:14)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 46,281

Re: Mensuration

Hi Relentless and bobbym,

Excellent, bobbym!

M#169. Using clay, a student made a right circular cone of height 48 cm and base area 12 cm. Another student reshapes it in the form of a sphere. Find the radius of the sphere.

---

It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Mensuration

Pshaw! Just because the bottom of the cylinder rests on the ground, it does not count as part of the surface area?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Mensuration

Hi;

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.