Area and Volume of Prisms and Pyramids

lisathedork · 2015-10-15 04:48:34

Hello, I need help with the following questions.

The shape is a pyramid with:

6. a rectangular base with a width of 4

7. a square base

8. a rectangular base with a width of 3

9. a rectangular base with a width of 5

10. a rectangular base with a width of 7

I have an isosceles triangle with a height of 4 and a base of 6:

11. What is the area?

This triangle just became the base of a regular prism, with a height of 8:

12. What is the lateral area?

13. What is the volume?

.

14. What is the area of the largest rectangular side?

I have a rectangle, with a length of 7 and a width of 4:

15. What is the perimeter?

16. What is the area?

This rectangle just became the base of a regular prism, with a height of 6:

17. What is the lateral area?

18. What is the total surface area?

19. What is the volume?

20. What is the area of the largest rectangular side?

Bob · 2015-10-16 01:22:02

hi Lisa,

The volume of any pyramid is one third of the (perpendicular) height times the area of the base.

Your questions don't have enough information.

eg Q6. The rectangular base has width 4. But what is the length ? And how high is the pyramid ?

Did you forget to post the whole question ? Perhaps the missing bits are further up the 'page'.

These following ones do have enough information:

I have an isosceles triangle with a height of 4 and a base of 6:

11. What is the area?

You can just do half the base times the height.

This triangle just became the base of a regular prism, with a height of 8:

12. What is the lateral area?

You need to work out the lengths of the equal sides using Pythagoras' theorem.

Then you can work out the three rectangular side areas and add them together: 8 x 6 + 8 x side + 8 x side.

13. What is the volume?

The volume of a prism is base area times height

.

14. What is the area of the largest rectangular side?

I have a rectangle, with a length of 7 and a width of 4:

15. What is the perimeter?

perimeter is length + width + length + width (distance all the way round)

16. What is the area?

Bob

lisathedork · 2015-10-20 12:58:56

Sorry for the late response!

I think this is the information you need.

For 1 through 10, what is the area and volume of the given shape, if the length of one side of the base is 6, the height is 8, and the slant height is 10? (Not all shapes will require all three numbers.)
The shape is a right prism with -

Bob · 2015-10-20 20:21:36

hi Lisa,

That's what I needed.

Q6 - Q10 are similar so I'll just take you though Q6.

Q6. Work out the area of the rectangular base. L = 6 W = 4 area = 6x4

Then do volume = 1/3 base area x height (=8)

The surface area is causing me a problem at the moment.

You've been given more information than you need. One of the measurements is inconsistent with the rest and this means there are two possible answers, depending on which numbers you use.

I've called three sides of the base, A, B and C. D is the midpoint of AB, and E is the midpoint of BC. F is the middle of the base, and G is the vertex of the pyramid.

To calculate the area of triangle GAB you need the base (AB = 6) and the height of the triangle (GD).

There are two ways to calculate GD. You can apply Pythagoras to triangle GDF in which case

Or you can use triangle GDB in which case

I'm asking for a 'second opinion' on this question.

Bob

SteveB · 2015-10-20 20:46:41

Yes I agree with you Bob, you get two different results for the length of GD so the information is over-constrained.

Bob · 2015-10-20 21:21:00

Further comment.

With any rectangular base (measurements known) and known height, you can calculate the sloping height as follows:

then

Thus is a mistake to give the sloping height too. Unless the questioner calculates this measurement and gives the correct value, consistent with the other measurements, the question is meaningless since there is no pyramid with those dimensions.

This is not the first time I have found questions from this course that have errors in them. It makes me wonder if the person who constructed them should have been doing so.

Best advice (if you want to continue paying these people money) is that you point out the error and say which value you are intending to use. Even then, that's no guarantee that you will get it marked right as I have also found that the markers are not always capable of spotting that the error is theirs and sometimes stick to their answer whatever.

I would use

ignoring the slope value completely.

Then the area of GAB is half 6 x GD.

You also need to calculate GE (it is not the same as GD) in a similar way to get the area of GBC.

The other two sloping faces are the same as GAB and GBC so you can double up your answers add in the base area and hopefully get the 'correct' surface area.

Q7. The base is a square so L=W. Otherwise it's the same sort of calculation to Q6. And the others are too.

Hope that hasn't confused you too much,

Bob

lisathedork · 2015-10-28 04:29:37

I'm still having trouble with the following questions. Can someone please guide me through this?

For 1 through 10, what is the area and volume of the given shape, if the length of one side of the base is 6, the height is 8, and the slant height is 10? (Not all shapes will require all three numbers.)

1. An equilateral triangle as the base.

This triangle just became the base of a regular prism, with a height of 8:
12. What is the lateral area?
13. What is the volume?
14. What is the area of the largest rectangular side?

This rectangle just became the base of a regular prism, with a height of 6:
17. What is the lateral area?
18. What is the total surface area?
19. What is the volume?
20. What is the area of the largest rectangular side?

Bob · 2015-10-28 09:24:42

hi Lisa,

11. An equilateral triangle as the base.

The triangle has all sides = 6, so half a side = 3, so by Pythagoras the height of the triangle is square root(36 - 9) = square root(27) = square root (9x3) = 3root(3)

So the area of the triangle half 6 x 3root(3) = 9root(3).

This triangle just became the base of a regular prism, with a height of 8:
12. What is the lateral area?

The sides of the prism are all rectangles 6 by 8, so the total are of the sides is 6 x 8 x 3.

13. What is the volume?

= area of base x height (8)

14. What is the area of the largest rectangular side?

?? They are all the same as above.

This rectangle just became the base of a regular prism, with a height of 6:

17. What is the lateral area?

Oh. what rectangle is this. Look up what you've been told are its measurements (L and W)

The lateral area is L x 6 (twice) + W x 6 (twice)

18. What is the total surface area?

Now add on the area of the base (L x W) twice.

19. What is the volume?

= L x W x 6

20. What is the area of the largest rectangular side?

Choose the two largest out of L, W and 6 and multiply them.

Hope that helps.

Bob

lisathedork · 2015-11-01 09:56:23

Thank you so much for the help! I'm now done with this math class.

Bob · 2015-11-01 20:21:55

hi Lisa,

You are welcome.

Best wishes for what you do next.

Bob

Math Is Fun Forum

#1 2015-10-15 04:48:34

Area and Volume of Prisms and Pyramids

#2 2015-10-16 01:22:02

Re: Area and Volume of Prisms and Pyramids

#3 2015-10-20 12:58:56

Re: Area and Volume of Prisms and Pyramids

#4 2015-10-20 20:21:36

Re: Area and Volume of Prisms and Pyramids

#5 2015-10-20 20:46:41

Re: Area and Volume of Prisms and Pyramids

#6 2015-10-20 21:21:00

Re: Area and Volume of Prisms and Pyramids

#7 2015-10-28 04:29:37

Re: Area and Volume of Prisms and Pyramids

#8 2015-10-28 09:24:42

Re: Area and Volume of Prisms and Pyramids

#9 2015-11-01 09:56:23

Re: Area and Volume of Prisms and Pyramids

#10 2015-11-01 20:21:55

Re: Area and Volume of Prisms and Pyramids

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