A hemispherical bowl has an external radius of 18cm and is made of wood 3m thick. calculate the volume of the wood in the bowl.
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For a (complete) sphere,
volume=(4/3)πr³
The volume of material is the volume of whole sphere (radius r2) minus the volume of empty spherical space (radius r1). The thickness t is the difference between r1 and r2, i.e.
r1+t=r2.
Vm=(4/3)π(r2³-r1³)
The volume of material for a hemisphere is half of that of the whole sphere.
A hemisphere bowl has an external radius of 18 cm and is made of wood 3cm thick
To calculate the volume of the wood in the bowl, we need to subtract the volume of the hollow cavity from the total volume of the hemispherical bowl.
Step 1: Calculate the volume of the hemispherical bowl.
The formula for the volume of a sphere is: V = (4/3)πr^3
Since a hemisphere is half of a sphere, we need to divide the volume by 2.
V_bowl = (1/2) * (4/3) * π * (18cm)^3
Step 2: Calculate the volume of the hollow cavity.
We need to calculate the volume of a smaller hemisphere, which is the cavity within the bowl. The radius of the smaller hemisphere can be obtained by subtracting the thickness of the wood from the external radius.
Radius of smaller hemisphere = External radius - Thickness of wood = 18cm - 3m = 15cm
V_cavity = (1/2) * (4/3) * π * (15cm)^3
Step 3: Calculate the volume of the wood.
Volume of wood = V_bowl - V_cavity
Now, let's plug the numbers into these formulas and calculate:
V_bowl = (1/2) * (4/3) * π * (18cm)^3
= (2/3) * π * (18cm)^3
V_cavity = (1/2) * (4/3) * π * (15cm)^3
= (2/3) * π * (15cm)^3
Volume of wood = V_bowl - V_cavity
= (2/3) * π * (18cm)^3 - (2/3) * π * (15cm)^3
= (2/3) * π * [(18cm)^3 - (15cm)^3]
Plug in the values and calculate the result to find the volume of the wood in the bowl.