Mathematics, 27.03.2021 21:50 gerardogonzale2294

A cone has radius 9 and a height 12. A frustum of this cone has height 4. What are the radii of the bases of the frustum?
What is the slant height of the frustum?
What is the lateral area of the frustum?

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Answer from: lupitasalas9283

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:

$\displaystyle \frac{12}{8}=\frac{9}{x}$

Solve for x. Simplify:

$\displaystyle \frac{3}{2}=\frac{9}{x}$

Cross-multiply:

$18=3x\Rightarrow x=6$

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:

SH^2=12^2+9^2

Simplify:

$SH^2=225\Rightarrow SH=15\text{ units}$

Now, find the slant height of the upper cone:

$(SH_\text{cone})^2=8^2+6^2=100$

So:

$SH_\text{cone}=10$

Then the slant height of the frustum will be the cone subtracted from the total. Thus:

$SH_{\text{frustum}}=15-10=5\text{ units}$

Part C)

We can first find the lateral area of the entire cone. The lateral area is given by:

$LA=\pi r\ell$

The lateral area of the entire cone will be:

$LA=\pi (9)(15)=135\pi$

The lateral area of the upper cone will be:

$LA_\text{cone}=\pi(6)(10)=60\pi$

Then the lateral area of the frustum is:

$LA_\text{frustum}=135\pi-60\pi =75\pi\text{ units}^2\approx235.62\text{ units}^2$

A cone has radius 9 and a height 12. A frustum of this cone has height 4.

What are the radii of the

Answer from: Quest

the answer would be c

Answer from: Quest

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max. it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to. the number combination of adults (x) and campers (y) cannot exceed this 525 max. therefore:

x + y ≤ 525

now we talk about cost. it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults. same with the campers, who cost $5 to feed. the adults can be represented by 9x and the campers can be represented by 5y. since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200

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A cone has radius 9 and a height 12. A frustum of this cone has height 4. What are the radii of the...