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.)

703.36 in ^ 3

Step-by-step 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

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.

i think its 7.6

if so your welcome