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sergij07 [2.7K]
4 years ago
6

A cone with height h and radius r has volume V = 13πr^2h. If the cone has a height of 6 in. and volume V = 8πx^2 + 24πx + 18π, w

hat is its radius r in terms of x?
Mathematics
2 answers:
torisob [31]4 years ago
5 0

ANSWER

r = x -  \frac{3}{2}

EXPLANATION

The volume of the cone is

V=8\pi \:  {x}^{2}  + 24\pi \: x + 18\pi

The height of the is 6 inches.

We put the values into the volume of cone to get.

8\pi \:  {x}^{2}  + 24\pi \: x + 18\pi =  \frac{1}{3} \times  \pi \:  {r}^{2}  \times 6

8\pi \:  {x}^{2}  + 24\pi \: x + 18\pi = 2 \pi \:  {r}^{2}

Divide through by 2π.

4 {x}^{2}  + 12x + 9 = {r}^{2}

The expression on the LHS is a perfect square trinomial.

( {x -  \frac{3}{2} })^{2}  =  {r}^{2}

r = x -  \frac{3}{2}

alukav5142 [94]4 years ago
5 0

Answer:

Its NOT r=3x+2

Step-by-step explanation:

srry, it doesnt tell me the correct answer. hope this helps

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The second condition is also satisfied.

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