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Yek
19.07.2019 •
Mathematics
In a cylinder the radius and height was quadrupled. how much bigger would the new surface area be then the original surface area.
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Ответ:
A = 2 * pi * r ^ 2 + 2 * pi * r * h
Where,
r: radio
h: height
The area when the dimensions are modified is:
A '= 2 * pi * (4r) ^ 2 + 2 * pi * (4r) * (4h)
Rewriting we have:
A '= 16 * 2 * pi * r ^ 2 + 16 * 2 * pi * r * h
A '= 16 (2 * pi * r ^ 2 + 2 * pi * r * h)
A '= 16A
the new surface area would be 16 times bigger than the original surface area
Ответ:
if in a cylinder the radius and height was quadrupled
so
the scale factor is equal to 4
scale factor=4
and
new surface area=[scale factor]²*original surface area
new surface area=[4]²*original surface area
new surface area=16*surface area original
therefore
the new surface area will be 16 times the original surface area.
alternative method
we know that
surface area of cylinder=2*[area of the base]+perimeter of the base*height
area of the base=pi*r²
perimeter of the base=2*pi*r
original surface area=2*[pi*r²]+[2*pi*r]*h> 2*pi*r*[r+h]
if the radius and height was quadrupled
so
new surface area=2*pi*(4*r)*[4r+4h]> 2*pi*(4*r)*4*[r+h]
new surface area=16*[2*pi*r*(r+h)]> 16*[original surface area]
the answer is
the new surface area will be 16 times the original surface area.
Ответ:
W(7) = 5(7) + 2
W(7) = 35 + 2
W(7) = 37