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3 years ago

If prism A and Prism B have a ratio of similarity of 2:3, what is the volume of prism A if Prism B's volume is 56 cubic inches

Mathematics

1 answer:

Sunny_sXe [5.5K]3 years ago

3 0

Answer:

16.6 in³

Step-by-step explanation:

Given the ratio of similarity = 2 : 3, then

the ratio of volumes = 2³ : 3³ = 8 : 27

let the volume of prism A be x then by proportion

$\frac{x}{8}$ = $\frac{56}{27}$ ( cross- multiply )

27x = 448 ( divide both sides by 27 )

x = 448 ÷ 27 ≈ 16.6 ( to 1 dec. place )

Prism A has a volume of approx 16.6 in³

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What is the length of the segment connecting the points A(1,3) and B(6,5)?

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Answer:

The answer is

<h2> $\sqrt{29} \: \: \: or \: \: \:5.38 \: \: \: units$ </h2>

Step-by-step explanation:

The length of the segment connecting two points can be found by using the formula

$d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(1,3) and B(6,5)

The length is

$|AB| = \sqrt{ ({1 - 6})^{2} + ({3 - 5})^{2} } \\ = \sqrt{ ({ - 5})^{2} + ( { - 2})^{2} } \\ = \sqrt{25 + 4} \\ = \sqrt{29}$

We have the final answer as

$\sqrt{29} \: \: \: or \: \: \:5.38 \: \: \: units$

Hope this helps you

3 0

3 years ago