Question

Estimate the volume of material in a cylindrical shell with height 32 ​in., radius 7 in. comma and shell thickness 0.5 in. Round to one decimal place.​ (Use 3.14 for pi​.)

Answer 1

703.36 in ^ 3

Explanation:

We have the following information:

Height (h) = 32 in

Radius (r) = 7 in

Thickness (dr) = 0.5 in

Now the volume of a cylinder is:

V π (r ^ 2) * h

if we derive with respect to the radius we are left with:

dV / dr = 2 * π * r * h

then solved for dV, we would have:

dV = 2 * π * r * h * dr

we know all these values so we replace:

dV = 2 * π * 7 * 32 * 0.5

dV = 224 * π

if we say that π is approximately 3.14

V = 703.36

Therefore the estimate of the volume of that cylinder is 703.36 in ^ 3