The Question is "Which container has the greater surface area?" and "How much more surface area does one have than the other?". It also told me to round to the nearest tenth.
The first container looks like this.
I found the surface area of this cylinder by making it's net, and then finding the surface area of the circle and rectangle.
The net of this cylinder looks like this ..
S.A of the circle = Pi x r squared
= Pi x 5 squared
= Pi x 25
= 78.5 squared cm
Before I could find the surface area of the rectangle in the net, I needed the formula for the diameter of the the circle which was ..
d of the circle = r x 2
= 5 x 2
= 10 cm
and the circumfrence of the circle for the other side of the rectangle.
C of the circle = Pi x d
= Pi x 10
=31.4 cm
Now that I found out the circumfrence of the circle, I can figure out the surface area of the rectangle in the net.
S.A of the rectangle = l x w
= 14 x 31.4
= 44 squared cm
So the TSA (total surface area) of the cylinder is ..
TSA = [2(S.A of cirlce)] + (Area of rectangle)
= [2(78.5)] + (44)
= 157 + 44
= 201 squared cm
The second container looked like this.
I found this shape's surface area by making it's net, and then adding the surface area for all three different sides, and the multiplied the answer by two.
This is what the net looks like ..
T.S.A of rectangular prism = 2(14 x 5) + (5 x 8) + (14 x 8)
= 2(70) + (40) + (112)
= 2 (222)
= 444 squared cm
I know the second container's surface area is more than the first container's surface area by 241 squared cm because 444 - 201 = 243 squared cm.
Thank you for reading my blog post.
Do not be afraid to help me learn by correcting me!
Good job! Your pictures are really easy to understand. I also like the colours, it's not too colorful but it looks good.
ReplyDeleteNicely done Brendan! I liked how you drew the net for each shape and how you included the dimensions as well. I would have to disagree with your answer for the finding the surface area of the cylinder. You should have used the formula: SA= 2πr² + 2πrh. Using that formula gives you a more accurate answer. *TIP: to get the actual pi symbol on your calculator you have to press shift then EXP. The actual answer should have been 596.9 cm² (rounded to the nearest tenth). The correct answer for the greater surface area was the first container since the it had an area of 596.9 cm² while the juice box had 444 cm². For the difference it should have been 152.9 cm². For the calculation for the juice box, you should have included the formula: SA= 2(lw) + 2(lh) + 2(hw), although your calculations were correct. You also could have added more colors to point out important informations or even bolded them. Otherwise, you explained your work very well and even if some of the answers were incorrect, you were able to support them with your own thinking.
ReplyDelete