A cone has a height of #36 cm# and its base has a radius of #9 cm#. If the cone is horizontally cut into two segments #24 cm# from the base, what would the surface area of the bottom segment be?
The surface area of the bottom segment
To explain this, I will show it with a diagram of a triangle as if the cone was vertically split.
We can find out the length of line now we know that: So we can now use the pythagorean theorem again to find out what We can also do the same equation as above to find out what Now that we have those measurements, we can substitute them in the Surface area equation.
By signing up, you agree to our Terms of Service and Privacy Policy
To find the surface area of the bottom segment of the cone after it has been horizontally cut 24 cm from the base, we need to calculate the surface area of the larger cone and subtract the surface area of the smaller cone.
First, we find the slant height of the larger cone using the Pythagorean theorem: [ l = \sqrt{h^2 + r^2} = \sqrt{36^2 + 9^2} = \sqrt{1296 + 81} = \sqrt{1377} ]
Next, we calculate the surface area of the larger cone: [ A_1 = \pi r_1 l_1 = \pi \times 9 \times \sqrt{1377} ]
Then, we find the slant height of the smaller cone (segment): [ l_2 = \sqrt{(h - 24)^2 + r^2} = \sqrt{(36 - 24)^2 + 9^2} = \sqrt{144 + 81} = \sqrt{225} = 15 ]
Now, we calculate the surface area of the smaller cone (segment): [ A_2 = \pi r_2 l_2 = \pi \times 9 \times 15 ]
Finally, we subtract the surface area of the smaller cone from the surface area of the larger cone to find the surface area of the bottom segment: [ A_{\text{bottom segment}} = A_1 - A_2 ]
[ A_{\text{bottom segment}} = \pi \times 9 \times \sqrt{1377} - \pi \times 9 \times 15 ]
[ A_{\text{bottom segment}} = \pi \times 9 \times (\sqrt{1377} - 15) ]
This gives us the surface area of the bottom segment of the cone.
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.
- A rectangular picture frame has a perimeter of 58 inches. The height of the frame is 18 inches. What is the width of the frame?
- A cone has a height of #24 cm# and its base has a radius of #5 cm#. If the cone is horizontally cut into two segments #16 cm# from the base, what would the surface area of the bottom segment be?
- If a hexagon has a radius of 6, what is its area?
- A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #39 # and the height of the cylinder is #17 #. If the volume of the solid is #150 pi#, what is the area of the base of the cylinder?
- Two corners of an isosceles triangle are at #(8 ,5 )# and #(6 ,1 )#. If the triangle's area is #12 #, 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