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2 years ago

Express 29 and 37 as the sum of two squares.

Mathematics

1 answer:

kotykmax [81]2 years ago

3 0

Answer:

See below

Step-by-step explanation:

${5}^{2} + {2}^{2} = 25 + 4 = 29 \\ \\ {6}^{2} + {1}^{2} = 36 + 1 = 37$

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cestrela7 [59]

We are given Volume of the larger cylinder is = 1600 cubic centimeters.

Height of the larger cylinder = 16 cm.

We know formula of volume of a cylinder V= $\pi r^2h$ , where r is the radius of cylinder, h is the height of the cylinder.

Plugging value of V and h of larger cylinder, we get

$1600=\pi r^2(16).$

Dividing both sides by 16, we get

$\frac{1600}{16}=\frac{\pi r^2 (16)}{16}$

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Taking square root on both sides, we get

r=10.

Therefore, radius of the larger cylinder is 10 cm.

We are given cylinders are similar .

<u>Note: The radii and heights of similiar cylinders are in same ratio.</u>

Therefore, we can setup a proportion:

Let us take radius of small cylinder is x.

$\frac{x}{10}=\frac{4}{16}$

$\frac{x}{10}=\frac{1}{4}$

Multiplying both sides by 10, we get

$10 \times \frac{x}{10}=10 \times\frac{1}{4}$

x=2.50.

Therefore, radius of the small cylinder = 2.5 cm.

Now, plugging radius =2.5 and height = 4 in the formula of volume the cylinder, we get

$V=\pi (2.5)^2(4)=\pi (6.25)(4) =25 \pi \ cm^3.$

Therefore, correct option is 25 pi cm^3.

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2 years ago

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