The radius of a 10 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.1 inch. use linear approximation or differentials to determine the possible error in the volume of the cylinder. include units in your answer.

502.4 ± 30.14 in^3

Step-by-step explanation:

r = 4 in, h = 10 in

error = ± 0.1 inch

Volume of a cylinder, V = π r² h

Take log on both the sides

log V = log π + 2 log r + log h

Differentiate both sides

dV/V = 0 + 2 dr/r + dh /h

dV/V = 2 (± 0.1) / 4 + (± 0.1) / 10

dV/V = ± 0.05 ± 0.01 = ± 0.06 (1)

Now, V = 3.14 x 4 x 4 x 10 = 502.4 in^3

Put in equation (1)

dV = ± 0.06 x 502.4 = ± 30.144

So, V ± dV = 502.4 ± 30.14 in^3

a) 32pie square meters

step-by-step explanation:

d 25 pi/6

step-by-step explanation:

the diameter is 10 inches

the radius is 1/2 of the diameter or 5 inches

the area of the circle is

a = pi r^2

  = pi 5^2

  = 25 pi

the slice is 60 degrees of the entire circle.

60 degrees out of 360   60/360 = 1/6

the area of the slice is 1/6 of the circle

a slice = 1/6 a circle

a slice = 1/6 * 25 pi