Mathematics, 20.07.2019 09:30 willowcollins3753

Acylinder container 18 inches tall and a diameter of 12 inches is completely filled with vanilla, chocolate, and strawberry ice cream in a ratio of 3: 2: 1. what is the volume of vanilla ice cream in the container? (round to nearest tenth) a) 339.3 in3 b) 678.6 in3 c) 1017.9 in3 d) 2035.8 in3

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Answers

If the diameter of the cylinder is 12 inches, then the radius is half that, or 6.

now, the flavors are on a ratio of 3:2:1, that simply means, we can just get the volume of the cylinder in total, and divide it by (3+2+1), and the vanilla flavor gets 3 of that quotient.

$\bf \textit{volume of a cylinder}\\\\
V=\pi r^2 h~~
\begin{cases}
r=radius\\
h=height\\
-----\\
h=18\\
r=6
\end{cases}\implies V=\pi (6^2)(18)\implies V=648\pi$

$\bf \stackrel{vanilla}{3}~~:~~\stackrel{chocolate}{2}~~:~~\stackrel{strawberry}{1}
\\\\\\
\stackrel{vanilla}{3\cdot \frac{648\pi }{3+2+1}}~~:~~\stackrel{chocolate}{2\cdot \frac{648\pi }{3+2+1}}~~:~~\stackrel{strawberry}{1\cdot \frac{648\pi }{3+2+1}}
\\\\\\
\stackrel{vanilla}{324\pi }~~:~~\stackrel{chocolate}{216\pi }~~:~~\stackrel{strawberry}{108\pi }$

Answer from: Quest

y = 2x

step-by-step explanation:

if you divide each number in the sequence, you'll see that they all have a multiple factor of 2. each number in the series, and any other numbers which may continue, will be multiplied by 2. therefore, y is the next number in the sequence, and x is the current one, so, our formula will be y = 2x.

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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