An ellipsoid has radii with lengths of #3 #, #4 #, and #7 #. A portion the size of a hemisphere with a radius of #3 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
THe answer is
By signing up, you agree to our Terms of Service and Privacy Policy
To find the volume of the remaining ellipsoid after removing a portion the size of a hemisphere with a radius of 3, we can use the formula for the volume of an ellipsoid:
[V = \frac{4}{3} \pi a b c]
Where (a), (b), and (c) are the semi-axes lengths of the ellipsoid.
Given that the ellipsoid originally has semi-axes lengths of 3, 4, and 7, and we remove a portion the size of a hemisphere with a radius of 3, the new semi-axes lengths will be 3, 4, and 4 (since the radius of the removed portion is the same as the semi-axis length of the ellipsoid).
Now we can calculate the volume of the remaining ellipsoid using the formula:
[V = \frac{4}{3} \pi \times 3 \times 4 \times 4]
[V = \frac{4}{3} \pi \times 48]
[V ≈ 64 \pi]
So, the volume of the remaining ellipsoid is approximately (64 \pi).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- How do you calculate the surface area of the lateral faces of a regular hexagonal pyramid that has a slant height of 35 cm and a base side length of 4 cm?
- A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 8 #. If one side of the triangle has a length of #15 #, what is the largest possible area of the triangle?
- The base of a triangular pyramid is a triangle with corners at #(6 ,5 )#, #(2 ,2 )#, and #(4 ,7 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?
- What is the perimeter of a rhombus-shaped highway sign with a 20-centimeter side?
- Two corners of an isosceles triangle are at #(5 ,2 )# and #(2 ,1 )#. If the triangle's area is #8 #, what are the lengths of the triangle's sides?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7