The volume of a hemispherical shell of outer radius 7 cm and inner radius 3.5 cm is
To find the volume of a hemispherical shell, we need to find the difference between the volumes of two hemispheres of different radii.
The volume of a hemisphere is given by the formula: V = (2/3) * π * r^3
First, we need to find the volume of the larger hemisphere with a radius of 7 cm.
V1 = (2/3) * π * 7^3
Next, we need to find the volume of the smaller hemisphere with a radius of 3.5 cm.
V2 = (2/3) * π * 3.5^3
Now, to find the volume of the hemispherical shell, we subtract the volume of the smaller hemisphere from the volume of the larger hemisphere.
Volume of hemispherical shell = V1 - V2
Let's calculate it:
V1 = (2/3) * π * 7^3
V1 = (2/3) * π * 343
V1 = 2π * 343/3
V1 ≈ 2405.06 cm^3 (rounded to two decimal places)
V2 = (2/3) * π * 3.5^3
V2 = (2/3) * π * 42.875
V2 = 2π * 42.875/3
V2 ≈ 150.80 cm^3 (rounded to two decimal places)
Volume of hemispherical shell = V1 - V2
Volume of hemispherical shell ≈ 2405.06 cm^3 - 150.80 cm^3
Volume of hemispherical shell ≈ 2254.26 cm^3 (rounded to two decimal places)
Therefore, the volume of the hemispherical shell with outer radius 7 cm and inner radius 3.5 cm is approximately 2254.26 cm^3.