Question

Direction: Below given a question and three statements numbered I, II and III. You have to decide whether the data provided in the statements are sufficient to answer the question. Read all the statements and give answer:A metal block of density ‘D’ and mass ‘M’, in the form of a cuboid, is beaten into a thin square sheet of thickness ‘t’, and rolled to form a cylinder of the same thickness. Find the inner radius of the cylinder –Statement I: Cuboid has dimensions 10cm x 5 cm x 12 cmStatement II: Thickness ‘t’ = 1.5cm Statement III: Mass of block, M = 216kg

• (A) Either statement III alone or statements I and II together are sufficient.
• (B) Only statement III is sufficient.
• (C) Statement I and Statement II together are sufficient.
• (D) Only statement I, II, and III together are sufficient.

Answer 1

The Correct Option is C

Explanation:
If we have the dimensions, from Statement a,Volume of cuboid $=10\times 5\times 12=600c{m}^3$If thickness is ' $t$ ' and let side of square sheet be $S$, then,$600=\left(S^2\right)\times (t)$If $t=1.5cm$ is taken from Statement II,$\frac{600}{1.5}=\left(S^2\right)=400$$S=20cm$Height of cylinder $=S=20cm$ [As square sheet is rolled so the side of the cylinder will be equal to side of square]Outer circumference $=S=20cm=2\pi r$Or, $r=\frac{10}{\pi }\approx 3.185$Thickness taken, $t=1.5cm$So inner radius $=3.185-1.5=1.685cm$Whereas Statement III has no significance anywhere.But none of the statement alone can answer the question individually.So, answer is using statement I and II together is sufficient
Hence, the correct option is (C).