Question

A rectangular sheet of metal is rolled along its length to form a cylinder of volume 269500 cm3and lateral surface area 15400 cm2. If the sheet would have been cut in two halves vertically dividing its length in 2:3 ratio and then these parts are rolled into two cylinders along their lengths, then find the sum of volume of both the cylinders formed and also find the difference between area of both parts of sheet when cut.

• A. 140144 cm³, 3080 cm²
• B. 141144 cm³, 3088 cm²
• C. 140140 cm³, 3080 cm²
• D. 141141 cm³, 3800 cm²
• E. 140000 cm³, 3000 cm²

Answer 1

The Correct Option is C

The length of the cylinder = circumference of the base of the cylinder
Let for cylinder, radius be 'r' cm
Breadth of the cylinder = height of the cylinder = 'h' cm
πr²h = 269500.... (i)
And, 2πrh = 15400
rh = 2450
Put in (i)
\(\frac{22}{7}\) * r * 2450 = 269500
r = 35 cm
so, h = \(\frac{2450}{35}\) = 70 cm = breadth
Now,
Length of rectangle = 2πr = 2*22*\(\frac{35}{7}\) = 220 cm
So, when the rectangle is cut in two halves, let one length L1 = 220*\(\frac{2}{5}\)= 88 cm
Other length L2 = 220*\(\frac{3}{5}\) = 132 cm
Difference in areas= 132*70 - 88*70 = 3080cm²
Radius of 1^st cylinder = r¹ = 2*\(\frac{35}{5}\) = 14 cm
Radius of 1^st cylinder = r² = 3*\(\frac{35}{5}\) = 21 cm
Height remains the same.
Sum of volumes = π{(r2)² + (r1)² }h = \(\frac{22}{7}\) *(14²+ 21²)* 70 = 140140 cm³
So the correct option is (C): 140140 cm³