Paint Roller A has a length of 12 in. and a diameter of 2 in. Paint Roller B has a length of 8 in. and a diameter of 3 in. Which roller can spread more paint on a wall in one revolution

Use the formula:

A = 2 * pi * r * h

a= 2 x 3.14x 1 x 12

a = 75.36

a = 2 x 3.14x 8 x 3

a= 150.71

roller B

In b, you used the diameter, not the radius.

2 * 3.14 * 1.5 * 8 = 75.36

They both cover the same amount of wall in one revolution.

To determine which roller can spread more paint on a wall in one revolution, we need to compare the surface areas of the two rollers.

First, let's calculate the surface area of roller A. The formula to calculate the surface area of a cylinder is given by:

Surface Area = 2πr(r + h),

where r is the radius of the base and h is the height (or length) of the cylinder.

For roller A:
Radius (r) = diameter/2 = 2 in / 2 = 1 in,
Height (h) = length = 12 in.

Surface Area of roller A = 2π(1 in)(1 in + 12 in) = 2π(1 in)(13 in) = 26π in².

Next, let's calculate the surface area of roller B using the same formula.

For roller B:
Radius (r) = diameter/2 = 3 in / 2 = 1.5 in,
Height (h) = length = 8 in.

Surface Area of roller B = 2π(1.5 in)(1.5 in + 8 in) = 2π(1.5 in)(9.5 in) = 28.5π in².

Now, we can compare the surface areas of the two rollers.

Surface Area of roller A = 26π in²,
Surface Area of roller B = 28.5π in².

Since the surface area of roller B is larger than the surface area of roller A, roller B can spread more paint on a wall in one revolution.