A hollow cylinder made of wood has an external radius of 14 cm, an internal…

The volume of material in a hollow cylinder equals the difference between the volumes of the outer (solid) cylinder and the inner (removed) cylinder: V = π(R2 − r2)h, where R is the external radius, r is the internal radius, and h is the height.

1. Identify the given values: external radius R = 14 cm, internal radius r = 7 cm, height h = 10 cm.

2. Square each radius: R2 = 142 = 196 and r2 = 72 = 49.

3. Find the difference of the two squares: R2 − r2 = 196 − 49 = 147.

4. Multiply the difference by the height: 147 × 10 = 1470, so the volume of wood is 1470π cm³.

As an independent check, find the two cylinder volumes separately and subtract: the outer cylinder's volume is πR2h = π × 196 × 10 = 1960π cm³, and the inner (removed) cylinder's volume is πr2h = π × 49 × 10 = 490π cm³. Subtracting gives 1960π − 490π = 1470π cm³, confirming the result.

So the volume of wood in the cylinder is 1470π cm³.