Case 1:
Cylinder along the length.
So, height of cylinder = length of rectangle = m
circumference = breadth = 10cm
So, C = 2πr
==>10 = 2πr
==>5 = πr
==>r = (5/π) cm
Volume of Cylinder 1 = π(r^2)h
= π * 5/π * 5/π * m = (25*m/π) cu.cm
Case 2:
Cylinder along the Breadth.
So, height of cylinder = breadth of rectangle = 10cm
circumference = length = m
==>m = 2πr
==>m/2 = πr
==>r = (m/2π) cm
Volume of Cylinder 2 = π(r^2)h
= π * m/2π *m/2π * 10 = (10[tex]m^2[/tex]/4π)cu.cm
Now,
Vol. 2 - Vol. 1 = 210
10[tex]m^2[/tex]/4π - 25*m/π = 210
10[tex]m^2[/tex]/4π - 100*m/4π = 210
10[tex]m^2[/tex] - 100m = 210*4π
10[tex]m^2[/tex] - 100m= 210 * 4 * 22/7 = 30 * 4 * 22 = 660 * 4 = 2640
10[tex]m^2[/tex] - 100m = 2640
[tex]m^2[/tex] - 10m= 264
[tex]m^2[/tex] - 10m - 264 = 0
[tex]m^2[/tex] - 22m + 12m - 264 = 0
m (m - 22) + 12 (m -22) = 0
(m + 12) (m-22) = 0
m = -12 or 22
Since m is the length it can not be negative.
So, m = 22
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Answers & Comments
Case 1:
Cylinder along the length.
So, height of cylinder = length of rectangle = m
circumference = breadth = 10cm
So, C = 2πr
==>10 = 2πr
==>5 = πr
==>r = (5/π) cm
Volume of Cylinder 1 = π(r^2)h
= π * 5/π * 5/π * m = (25*m/π) cu.cm
Case 2:
Cylinder along the Breadth.
So, height of cylinder = breadth of rectangle = 10cm
circumference = length = m
So, C = 2πr
==>m = 2πr
==>m/2 = πr
==>r = (m/2π) cm
Volume of Cylinder 2 = π(r^2)h
= π * m/2π *m/2π * 10 = (10[tex]m^2[/tex]/4π)cu.cm
Now,
Vol. 2 - Vol. 1 = 210
10[tex]m^2[/tex]/4π - 25*m/π = 210
10[tex]m^2[/tex]/4π - 100*m/4π = 210
10[tex]m^2[/tex] - 100m = 210*4π
10[tex]m^2[/tex] - 100m= 210 * 4 * 22/7 = 30 * 4 * 22 = 660 * 4 = 2640
10[tex]m^2[/tex] - 100m = 2640
[tex]m^2[/tex] - 10m= 264
[tex]m^2[/tex] - 10m - 264 = 0
[tex]m^2[/tex] - 22m + 12m - 264 = 0
m (m - 22) + 12 (m -22) = 0
(m + 12) (m-22) = 0
m = -12 or 22
Since m is the length it can not be negative.
So, m = 22
Hope It Helps
Please Mark Me As Brainliest.