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a. Volume stays the same
b. Volume is 3 times bigger
c. Volume is 9 times bigger
d. Volume is 27 times bigger
(1pt.) Cylinder A is similar to Cylinder B. The ratio of the surface areas from
A to
B is
4:9. If the volume of Cylinder A is
1000in^(3), what is the volume of Cylinder
B ?
9
What is the volume of Cylinder B?

a. Volume stays the same $\newline$ b. Volume is $3$ times bigger $\newline$ c. Volume is $9$ times bigger $\newline$ d. Volume is $27$ times bigger $\newline$ ( $1$ pt.) Cylinder A is similar to Cylinder B. The ratio of the surface areas from $A$ to $B$ is $4: 9$ . If the volume of Cylinder A is $1000 \mathrm{in}^{3}$ , what is the volume of Cylinder $\mathrm{B}$ ? $\newline$ $9$ $\newline$ What is the volume of Cylinder B?

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Evaluate a linear function: word problems

Full solution

Q. a. Volume stays the same

\newline

b. Volume is

3

times bigger

\newline

c. Volume is

9

times bigger

\newline

d. Volume is

27

times bigger

\newline

(

1

pt.) Cylinder A is similar to Cylinder B. The ratio of the surface areas from

A

to

B

is

4: 9

. If the volume of Cylinder A is

1000 \mathrm{in}^{3}

, what is the volume of Cylinder

\mathrm{B}

?

\newline

9

\newline

What is the volume of Cylinder B?

Identify Relationship: Identify the relationship between the surface areas and the volumes of similar cylinders. Since the cylinders are similar, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions. Given the surface area ratio is $4:9$ , the linear dimension ratio is the square root of $4:9$ , which is $2:3$ .
Calculate Volume Ratio: Calculate the volume ratio using the linear dimension ratio. The volume ratio is the cube of the linear dimension ratio, so $(\frac{2}{3})^3 = \frac{8}{27}$ .
Calculate Volume of Cylinder B: Calculate the volume of Cylinder B using the volume ratio. Multiply the volume of Cylinder A by the volume ratio: $1000 \, \text{in}^3 \times \left(\frac{8}{27}\right) = 296.296296 \, \text{in}^3$ .

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