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.
volume of wood
= (4/3)π(18^3) - (4/3)π(15^3)
= .....
The question would be more interesting if there was an opening with some dimension so that
you can something in the bowl.
the bowl is a hemisphere, so cut those values in half.
To calculate the volume of the wood in the bowl, we need to find the difference between the volume of the outer hemisphere and the volume of the inner hemisphere.
The volume of a hemisphere is given by the formula:
V = (2/3) * π * r^3
where V is the volume and r is the radius.
First, let's calculate the volume of the outer hemisphere:
V_outer = (2/3) * π * (18cm)^3
Now, we need to calculate the volume of the inner hemisphere. The radius of the inner hemisphere can be calculated by subtracting the thickness of the wooden bowl from the external radius:
r_inner = 18cm - 3m = 180cm - 300cm = -120cm
However, a negative radius is not valid, so there is no volume for the inner hemisphere. Therefore, we can say that the total volume of the wood in the bowl is equal to the volume of the outer hemisphere:
V_wood = V_outer
Now, let's substitute the values and calculate the volume of the wood in the bowl:
V_wood = (2/3) * π * (18cm)^3
= (2/3) * 3.14 * (18cm)^3
≈ 12137.04 cm³
So, the volume of the wood in the bowl is approximately 12137.04 cm³.
To calculate the volume of the wood in the bowl, we need to find the difference between the volume of the entire bowl and the volume of the hollow hemisphere inside.
To begin, we can calculate the volume of the entire bowl using the formula for the volume of a hemisphere, which is (2/3) * π * r^3, where r is the radius.
Given that the external radius of the bowl is 18 cm, we can substitute this into the formula:
Volume_of_bowl = (2/3) * π * (18 cm)^3
Now, let's calculate the volume of the hollow hemisphere inside the bowl. We can consider this as the volume of a smaller hemisphere that has a radius equal to the external radius minus the thickness of the wood.
The thickness of the wood is given as 3 m, which is equal to 300 cm. Therefore, the internal radius of the hollow hemisphere will be:
Internal_radius = External_radius - Wood_thickness = 18 cm - 300 cm = -282 cm
Since we cannot have a negative radius, it means that the thickness of the wood is greater than the external radius of the bowl, which is not physically possible. Please double-check the values provided.
If you have the correct values, make sure the units are consistent and try the calculation again.