The modified area is (1/48) (2πr(4h+3r))
<u>Step-by-step explanation:</u>
Let the radius be 'r' and height be 'h'.
Area of cylinder= 2π r(h+r)
The radius is shrunk down to quarter of its original radius
r = r/4
The height is reduced to a third of its original height
h = h/3
New Area = 2π(r/4) [(h/3) +(r/4) ]
= (1/4)2πr[(4h+3r) /12]
= (1/48) (2πr(4h+3r))
(x-3)2+(y-4)2=24
2x-6+2y=24
2x-14+2y=24
2x=24+14-2y
2x=38-2y
x=19-y
<span>MNO is similar to GHK by AA Similarity Postulate
Let's start by listing each triangle and the measurements of all three angles. For each triangle, we've been given the measurements of 2 of the angles and the 3 angle will simply be 180 minus the other 2 angles. I assume you can do the subtraction, so I'll simply list each triangle with all three angle measurements.
NMO: 79, 22, 79
GHK: 79, 79, 22
PQR: 20, 79, 81
DEF: 82, 22, 76
And the triangles NMO and GHK are similar to each other since they have the same angles. The order really doesn't matter since it's OK for similar triangles to be rotated or reflected. The key thing to remember in a triangle is that if you've been told what 2 of the angles are, you also know what the 3rd angle is since the sum of the angles of a triangle will always be 180.
So the answer is:
MNO is similar to GHK by AA Similarity Postulate"</span>
