Hey I'm Chloe can you help me, I will give Brainlest :) Thank you :)
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Answer:
Part A)
The lower base has a radius of 9 units, and the upper base has a radius of 6 units.
Part B)
5 units.
Part C)
75π or about 235.62 square units.
Step-by-step explanation:
Please refer to the figure below.
The cone has a radius of 9 units and a total height of 12 units.
A frustum of the cone has a height of 4 units.
Part A)
The lower radius of the frustum will simply be 9 units.
For the upper radius, we will use the properties of similar triangles. We will compare the smaller upper triangle to the overall larger triangle. This yields:
Solve for <em>x.</em> Simplify:
Cross-multiply:
The upper base has a radius of 6 units.
Part B)
We can first find the total slant height of the entire cone. By using the Pythagorean Theorem, this yields that the total slant height is:
Simplify:
Now, find the slant height of the upper cone:
So:
Then the slant height of the frustum will be the cone subtracted from the total. Thus:
Part C)
We can first find the lateral area of the entire cone. The lateral area is given by:
The lateral area of the entire cone will be:
The lateral area of the upper cone will be:
Then the lateral area of the frustum is:
