Mensuration Word Problems

[12345786332]

Unsure on how to solve. Please help. Questions down below.

 

[Deleted member 4993]

Unsure on how to solve. Please help. Questions down below.View attachment 20447

View attachment 20448

Please show us what you have tried and exactly where you are stuck.​

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Please follow the rules of posting in this forum, as enunciated at:​

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https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

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Please share your work/thoughts about this assignment.​

 

[Dr.Peterson]

For #8, I'd start by drawing in radii to each point of tangency.

For #7, I might label each of the four regions, and find the areas of a few sums of those regions (e.g. the whole quarter-circle), assuming some value for the radius (1 or 2 or "r", for example).

 

[HallsofIvy]

For 8 if you draw the radii as Dr. Peterson suggests, you divide the figure into 6 triangles, each with "base" length 50/6= 25/3 cm.. Further, the vertex angle has measure 360/6= 60 degrees. And the base angles are equal so each has measure (180- 60)/2= 120/2= 60 degrees also. They are equilateral triangles! What does that tell you about the length of each radius? And what does that tell you about the radius of each pipe?

 

[Deleted member 4993]

For 8 if you draw the radii as Dr. Peterson suggests, you divide the figure into 6 triangles, each with "base" length 50/6= 25/3 cm.. Further, the vertex angle has measure 360/6= 60 degrees. And the base angles are equal so each has measure (180- 60)/2= 120/2= 60 degrees also. They are equilateral triangles! What does that tell you about the length of each radius? And what does that tell you about the radius of each pipe?

I think you should get 6 "pie" slices and 6 rectangles. The band is tangential to the pipes, but "hugs" for a while!

 

[Steven G]

I think you should get 6 "pie" slices and 6 rectangles. The band is tangential to the pipes, but "hugs" for a while!

6 rectangles? I think that you have been spending too much time in the corner. I think that you should go sit in the triangle for a bit.

Are you suggesting because of the hugging that Sir HallsofIvy is wrong?

 

[Deleted member 4993]

6 rectangles? I think that you have been spending too much time in the corner. I think that you should go sit in the triangle for a bit.

Are you suggesting because of the hugging that Sir HallsofIvy is wrong?

Yes - the band is not touching the pipes at 6 points - instead it is hugging around 6 arcs. Each pipe will have 2 points of tangency with the band.

If the pipe-diameter is 'd', then the length of the band is (πd + 6d).

 

[pka]

For #7 There are three circles, one large of radius \(R\) and two small with radius \(\frac{1}{2}R\).
Prove that the sum of the areas of the smaller semicircles equals the area of the quarter of the larger circle.
Then think carefully how the semicircles fit together so the two green areas are equal.

 

[Deleted member 4993]

Yes - the band is not touching the pipes at 6 points - instead it is hugging around 6 arcs. Each pipe will have 2 points of tangency with the band.

If the pipe-diameter is 'd', then the length of the band is (πd + 6d).

@Jomo - are you at the corner of the rectangle yet!!!!!!