full label: circumference (C) × height (H) Given: actual label = 1/3 full label can Tall (H) = 6" Width (D) = 4" circle geometry C = pi × D can C: C = pi × 4 = 4pi Full Label = 4pi × 6 = 24pi 1/3 yields = (1/3)(24in^2)pi = (8in^2)pi
Well, The curved surface area of the Can (I assume it is cylindrical) : 2πrh given : d = 4 inch, r = d/2 = 4/2 = 2 inch, h = 6 inch Curved Surface area Can = 2π·2·6 = 24π inch² Surface area of the Label = 1/3 · 24π = 8π inch² ✅
24 times pi is 24 x 22/7=75.42857142857143 full surface of exterior of can this divided by three is label area or 25.14285714285714....... 8 pi r is 8 X 22/7 or the same result (25.14285714285714.......). Many different ways to get there all work for those who use them.
You could save yourself a divide by 2 immediately followed by a multiply by 2 there. We're given the diameter so you can just use πdh instead of dividing d by 2 and then using 2πrh.
Since I know it's a can, I just assume the shape is cylindrical( the 6in height gave it away too). So I just got the surface area of a cylinder and divided the answer by 3. 1/3(πd²h/4) or 1/3(πr²h)
If the can is 4 inches wide, that means the diameter of the can is 4 inches. The circumference of the can= 2 π r = diameter times π 4π = 4 x 22/7 = 88/7 inches (π = 22/7) The height of the can = 6 inches The entire area of the side of the can = Circumference of the can x height of the can = 88/7 x 6 square inches. The label covers 1/3rd of the side of the can. Therefore, the surface area of the label = 1/3 x 88/7 x 6 = 176/7 = 25 1/7 square inches. ~25.14 square inches.
other than I used Diameter Pie instead of two Pie R, I did it the same and got the same answer rounded to hundredths of the square inch. approximately 25.14 inches squared.
@@russelllomando8460 Yes, you are correct. I had the information of circumference = 2πr in my memory and was not thinking smart enough to realize that 2r is diameter and I could use the diameter directly, without finding the radius. Sometimes, my brain doesn’t perform sharp enough and makes silly mistakes. I notice some weaknesses in my memory and the functioning of the brain recently, probably the old age of going on my 75, must be contributing to it. However, I can’t use it as an excuse. But, following these videos of Mr John’s mathematics helps me going through life!
24 in^2. The question said 4 in wide, 6 in tall. If it was talking about the can, it would have said "diameter" or "circumference", so the 4 in must be talking about the width of the label. 6*4=24. Done.
Circumference is 4x Pi, so the label is 4Pi*6/3 = 8Pi = 25.13 approx.
Diameter = 4 in
Circumference = πd = 4π in
Area of the side of the can = circumference × height = 24π in²
Area of the label is ⅓ of that = 8π in²
full label:
circumference (C)
× height (H)
Given:
actual label = 1/3 full label
can
Tall (H) = 6"
Width (D) = 4"
circle geometry
C = pi × D
can C:
C = pi × 4
= 4pi
Full Label
= 4pi × 6
= 24pi
1/3 yields
= (1/3)(24in^2)pi
= (8in^2)pi
Well, The curved surface area of the Can (I assume it is cylindrical) : 2πrh
given : d = 4 inch, r = d/2 = 4/2 = 2 inch, h = 6 inch
Curved Surface area Can = 2π·2·6 = 24π inch²
Surface area of the Label = 1/3 · 24π = 8π inch² ✅
24 times pi is 24 x 22/7=75.42857142857143 full surface of exterior of can this divided by three is label area or 25.14285714285714.......
8 pi r is 8 X 22/7 or the same result (25.14285714285714.......). Many different ways to get there all work for those who use them.
You could save yourself a divide by 2 immediately followed by a multiply by 2 there.
We're given the diameter so you can just use πdh instead of dividing d by 2 and then using 2πrh.
Since I know it's a can, I just assume the shape is cylindrical( the 6in height gave it away too). So I just got the surface area of a cylinder and divided the answer by 3. 1/3(πd²h/4) or 1/3(πr²h)
6x4 = 24
x 3.14 = 75.36
divided by 3 = 25.12
If the can is 4 inches wide, that means the diameter of the can is 4 inches.
The circumference of the can=
2 π r = diameter times π
4π = 4 x 22/7
= 88/7 inches
(π = 22/7)
The height of the can = 6 inches
The entire area of the side of the can =
Circumference of the can x height of the can
= 88/7 x 6 square inches.
The label covers 1/3rd of the side of the can.
Therefore, the surface area of the label =
1/3 x 88/7 x 6 = 176/7 =
25 1/7 square inches.
~25.14 square inches.
other than I used Diameter Pie instead of two Pie R, I did it the same and got the same answer rounded to hundredths of the square inch. approximately 25.14 inches squared.
@
Yes, you are correct.
I didn’t have to find the radius.
The diameter was already given, as the width.
Circumference = diameter x π
@@chrisdissanayake6979 Both methods are correct. They both got the correct answer!
just to say.....2 Pi R is the same as Pi D you already have the D = 4
nice work
@@russelllomando8460
Yes, you are correct.
I had the information of circumference = 2πr in my memory and was not thinking smart enough to realize that 2r is diameter and I could use the diameter directly, without finding the radius.
Sometimes, my brain doesn’t perform sharp enough and makes silly mistakes.
I notice some weaknesses in my memory and the functioning of the brain recently, probably the old age of going on my 75, must be contributing to it.
However, I can’t use it as an excuse. But, following these videos of Mr John’s mathematics helps me going through life!
I can't multiply by PI in my head...
What’s wrong with (6x4):3x3.14
(pi • 4 • 6 ÷ 3) in²
can you leave a math question at every end of you vidoes to check for understanding ❤
got 25.12 Pi X 4 = 12.56 X 6 = 75.36 / 3 = 25.12 thanks for ther fun
= 25.13 inches square
25.14 sq.inches
Why doubt .its 8π
24 in^2. The question said 4 in wide, 6 in tall. If it was talking about the can, it would have said "diameter" or "circumference", so the 4 in must be talking about the width of the label. 6*4=24. Done.
I'm just concerned why you used the term "wide" for the diameter of the can.
8π?