Consider the following statements:

I. If the height of a cylinder is doubled, the area of the curved surface is doubled.

II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

Which of the above statement(s) is / are true:

Consider the following statements:

I. If the height of a cylinder is doubled, the area of the curved surface is doubled.

II. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

---

Statement I: If height of cylinder is doubled, curved surface area is doubled

Curved Surface Area of cylinder = $2\pi rh$ where $r$ is radius and $h$ is height.

Original CSA = $2\pi rh$

When height is doubled, new height = $2h$

New CSA = $2\pi r(2h)$

New CSA = $4\pi rh$

New CSA = $2 \times (2\pi rh)$

New CSA = $2 \times$ Original CSA

Statement I is true. The curved surface area depends directly on height, so doubling the height doubles the surface area.

---

Statement II: If radius of hemisphere is doubled, total surface area becomes fourfold

Total Surface Area of hemisphere = Curved surface + Flat circular base

Curved surface = $2\pi r^2$

Base area = $\pi r^2$

TSA = $2\pi r^2 + \pi r^2$

TSA = $3\pi r^2$

Original TSA = $3\pi r^2$

When radius is doubled, new radius = $2r$

New TSA = $3\pi(2r)^2$

New TSA = $3\pi(4r^2)$

New TSA = $12\pi r^2$

New TSA = $4 \times (3\pi r^2)$

New TSA = $4 \times$ Original TSA

Statement II is true. When the radius is doubled, the area formulas contain $r^2$, so $(2r)^2 = 4r^2$, resulting in 4 times the area.

---

Both statements are true.

Therefore, the answer is Both I & II.