Mathematics: Acone 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, what is its radius r in terms of x?

Acone with height h and radius r has volume v = 13πr^2h.

anikabarnhart

06.01.2022

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.

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

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

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ndkjfgj4368

11.09.2020

1, -1, negative reciprocals, parallel

Step-by-step explanation:

i just did it edge 2020

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