To calculate the volume (V) of a cylindrical shell:
V = (R^2 - r^2) * L * π
Where:
To calculate the total surface area (A) of a shell:
A = 2 * π * (R + r) * (R - r + L)
Where:
A cylindrical shell is defined as any hollowed-out cylinder that contains an inner diameter and an outer diameter. This is also considered a tube.
Let's assume the following values:
Using the formulas:
Volume (V) = (5^2 - 3^2) * 10 * π = (25 - 9) * 10 * π = 160 * π ≈ 502.65 cubic units
Surface Area (A) = 2 * π * (5 + 3) * (5 - 3 + 10) = 2 * π * 8 * 12 = 192 * π ≈ 603.19 square units
The volume is approximately 502.65 cubic units and the surface area is approximately 603.19 square units.
Let's assume the following values:
Using the formulas:
Volume (V) = (7^2 - 4^2) * 15 * π = (49 - 16) * 15 * π = 495 * π ≈ 1554.13 cubic units
Surface Area (A) = 2 * π * (7 + 4) * (7 - 4 + 15) = 2 * π * 11 * 18 = 396 * π ≈ 1244.07 square units
The volume is approximately 1554.13 cubic units and the surface area is approximately 1244.07 square units.