Area = πr²; if r is doubled, area = π(2r)² = 4πr², so it quadruples.

The area of a circle is given by A = πr². If the radius is doubled (r becomes 2r), the new area is A' = π(2r)² = 4πr², which is four times the original area.

Circumference = 2πr; If r is halved, new circumference = πr; Factor = 1/2.

Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.

Circumference = 2πr. If radius is halved, new circumference = 2π(r/2) = πr, which is halved.

Area increases by a factor of (3r)²/r² = 9.

Area = πr². If radius is tripled, new area = π(3r)² = 9πr², which is 9 times the original area.

The magnetic field at the center of a circular loop is inversely proportional to the radius; thus, doubling the radius halves the magnetic field.

The magnetic field at the center of a circular loop is given by B = (μ₀I)/(2r). If the radius is doubled, the magnetic field strength is halved.

The magnetic field at the center is inversely proportional to the radius, so it quadruples.

The moment of inertia of a disc is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is quadrupled.

The moment of inertia of a disk is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is 4 times the original.

If the radius is halved, the gravitational acceleration becomes four times stronger, as g is inversely proportional to the square of the radius.

g ∝ 1/R². If R is halved, g becomes 4 times greater.

Angular momentum L = Iω; if radius is doubled, moment of inertia I increases by a factor of 4, hence L quadruples.

Linear velocity v = rω. If r is halved and ω remains constant, v also halves.

Linear velocity v = rω, so if r is halved and ω remains constant, v also halves.

Moment of inertia I is proportional to the square of the radius, so halving the radius reduces I to one-fourth.

Linear velocity v = rω; if r is halved and ω remains constant, v is halved.

The moment of inertia of a solid disk is I = 1/2 MR^2. If R is doubled, I becomes 1/2 M(2R)^2 = 2MR^2, which is 4 times the original.

The electric field E due to a point charge decreases with the square of the distance from the charge, so if the radius is doubled, the electric field halves.

The electric field E due to a point charge decreases with the square of the distance from the charge, so if the radius is doubled, the electric field halves.

The electric field due to a point charge is independent of the radius of the Gaussian surface; it remains the same.

The focal length (f) of a concave mirror is given by f = R/2, where R is the radius of curvature. Thus, f = 20 cm / 2 = 10 cm.

The focal length f of a mirror is given by f = R/2. Thus, f = 40 cm / 2 = 20 cm.

The focal length f of a lens is given by f = R/2. Therefore, f = 20 cm / 2 = 10 cm.

The focal length (f) of a mirror is given by f = R/2. For a convex mirror, R is positive, so f = 20 cm / 2 = 10 cm.

The focal length f of a mirror is given by f = R/2. For a convex mirror, R = 30 cm, so f = 30/2 = 15 cm.

Using the lens maker's formula, f = R/(n-1) = 20/(1.5-1) = 40 cm.

Using the lens maker's formula, f = R/(n-1) = 30/(1.5-1) = 30/0.5 = 60 cm.