By applying force on an uniform metallic wire, the wire is extended four times along its length with same width all around. Then :

(i) The volume of metal in both the cases is same.

(ii) The surface area of solid wires in both the cases is same.

Which of the above statements is/are true?

1. only (i)

2. only (ii)

3. both (i) and (ii)

4. neither (i) nor (ii)

The given figure shows a toy made of very thin metal sheet. The toy has the hemisphere, a cylinder and a cone all of the same radius.

Assertion(A): The minimum area of metal sheet required is:

Curved surface area of conical part + curved surface area of cylinder part - curved surface area of hemispherical part

Reason(R): Metal sheet required = curved surface area of (conical part + cylindrical part + hemispherical part)

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

A solid cone of height 3 cm and radius 3 cm is recast into solid cylinder each of height 1 cm and radius 1 cm.

Assertion(A): Number of cylinders formed = $\dfrac{1}{3}$ x 3 x 3 x 3

Reason(R): Number of cylinders formed = $\dfrac{\dfrac{1}{3}π(3)^2 \times 3}{π(1)^2 \times 1}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

A solid wooden cylinder is of height h cm and radius r cm. A conical cavity of same height and the same radius is drill out of the solid cylinder.

Statement (1): The volume of the remaining wood = volume of the solid cylinder - volume of the cone drilled.

Statement (2): The volume of the remaining wood = πr²h - $\dfrac{1}{3}$ πr²h = $\dfrac{2}{3}$ πr²h

1. Both the statement are true.

2. Both the statement are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.