Two cylinder cans have the same volume. One can is triple the height of the other. If the narrow can has a radius of 12 inches, what is the radius of the wider can?

zabuheljz
2022-08-08
Answered

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Cynthia George

Answered 2022-08-09
Author has **10** answers

$volume=\pi h{r}^{2}$

so can1=can2

and in order to be the same the tall one must have a narrowerradius so

$3h\pi {12}^{2}=h\pi {r}^{2}$

h and $\pi $ cancel

$432={r}^{2}>>>r=20.78$

so can1=can2

and in order to be the same the tall one must have a narrowerradius so

$3h\pi {12}^{2}=h\pi {r}^{2}$

h and $\pi $ cancel

$432={r}^{2}>>>r=20.78$

Sydney Stein

Answered 2022-08-10
Author has **3** answers

: LET WIDE CAN RADIUS BE R,NARROW BE r.

HEIGHT OFWIDE CAN BE H,NARROW BE h

VOLUME:WIDE CAN=NARROW CAN

$\pi {R}^{2}H=\pi {r}^{2}h$

${R}^{2}H={r}^{2}h$

${R}^{2}H={r}^{2}3H$

${R}^{2}=3{r}^{2}$

${R}^{2}=3\ast 144$

$R=\sqrt{3}\ast 12$

R=1.732*12=20.784(Ans)

HEIGHT OFWIDE CAN BE H,NARROW BE h

VOLUME:WIDE CAN=NARROW CAN

$\pi {R}^{2}H=\pi {r}^{2}h$

${R}^{2}H={r}^{2}h$

${R}^{2}H={r}^{2}3H$

${R}^{2}=3{r}^{2}$

${R}^{2}=3\ast 144$

$R=\sqrt{3}\ast 12$

R=1.732*12=20.784(Ans)

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When I do this, I get $\frac{\pi}{5}$. The answer is $\frac{\pi}{8}$. What am I doing wrong?

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For this I use the disk formula. So $\pi {\displaystyle {\int}_{0}^{1}(\sqrt{x}{)}^{2}\phantom{\rule{thinmathspace}{0ex}}dx.}$.

When I do this, I get $\frac{\pi}{5}$. The answer is $\frac{\pi}{8}$. What am I doing wrong?

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F-I $5800-$6400

J-L $6500-$7100

M-O $7200-$7800

P-R $7800-$8500

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7. Your monthly cost is then, W = -.01x^2+100x+c.

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2. You will use: W=-.01x2+100x+c where (-.01x2+100x) represents the store's variable costs and c is the store's fixed costs.

3. So, W is the stores total monthly costs based on the number of items sold, x.

4. Think about what the variable and fixed costs might be for your fictitious storefront business - and be creative. Start by choosing a fixed cost, c, between $5,000 and $10,000, according to the following class chart:

5. My last name is Haggins so my fixed cost would be be between $5800-$6400

If your last name starts with the letter Choose a fixed cost between

A-E $5000-$5700

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J-L $6500-$7100

M-O $7200-$7800

P-R $7800-$8500

S-T $8600-$9200

U-Z $9300-$10,000

6. Post your chosen c value in your subject line, so your classmates can easily scan the discussion thread and try to avoid duplicating your c value. (Different c values make for more discussion.)

7. Your monthly cost is then, W = -.01x^2+100x+c.

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9. Next, choose two values of x (number of items sold) between 100 and 200. Again, try to choose different values from classmates.

10. Plug these values into your model for W and evaluate the monthly business costs given that sales volume.

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First I found the limits of integration by finding the points of intersection. They are (-1,1) and (4,16). I then found the radius from the axis of rotation to be $r=4-x$ and the height to be $h=3x+4-{x}^{2}$.

I used the Volume formula ${\int}_{a}^{b}2\pi (radius)(height)dx$.

$V={\int}_{-1}^{4}2\pi (4-x)(3x+4-{x}^{2})dx$

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