Thursday, October 7, 2010

Argie's blog post.

Okay, well today in class we were all assigned questions to make a blog about. My question was question number 19 from chapter 1.3 in our math textbooks.

The question was:
A party planner buys two plain cakes for a meal she is planning. One cake is square and the other is round. Both cakes are 6 cm think. The square cake measures 25 cm along each edge. The round cake has a diameter of 25 cm.
A) Sketch and label a diagram of each cake
B) Show how to make four cuts to create eight equal pieces for each cake.
C) Estimate and then calculate how much the surface area increases after each cake is cut and the pieces are slightly separated.



C) First you have to find the surface area of the whole rectangular prism.
SA = 2(lxw)+2(lxh)+2(wxh)
= 2(25x25)+2(25x6)+2(25x6)
= 2(625)+2(150)+2(150)
= 1250+300+300
= 1850 squared cm

Now you have to cut the rectangular prism into 8 equal pieces. So you divide the 25 by 8 because you are cutting it into 8 pieces.

Now find the surface area of one of those pieces.
SA = 2(lxw)+2(lxh)+2(wxh)
= 2(25x3.125)+2(25x6)+2(3.125x6)
= 2(78.125)+2(150)+2(18.75)
= 156.25+300+37.5
= 493.75 squared cm

After that has been done you have to multiply that answer by 8 because there are 8 pieces.
493.75x8=3950 squared cm

The surface area of the rectangular prism with the 8 equal pieces cut would be 3950 squared cm.

Since we just finished the rectangular prism, now the cylinder.

To find the surface area of this particular cylinder you do this...
First you need to get the radius from the diameter
r = d/2
r = 25/2
r = 12.5 cm

Now to find the surface area
SA = 2 x pi x r2 + 2 x pi x r x h
= 2 x 3.14 x 12.5 2 + 2 x 3.14 x 12.5 x 6
= 98.125 + 471
= 569.125 squared cm

Now that you have the surface area you now have to cut it into 8 pieces. So you divide the diameter by 8 to get 3.125

Now to get the surface area of the 8 slices

SA = 2 x pi x r2 + 2 x pi x r x h
= 2 x 3.14 x 3.125 2+ 2 x 3.14 x 3.125 x 6
= 61.33 +

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