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3 years ago

These cylinders are similar. Find the surface area of the smaller cylinder. Round to the nearest tenth.

Mathematics

1 answer:

GarryVolchara [31]3 years ago

5 0

Answer:

Surface area = 80.4 cm²

Step-by-step explanation:

The diagram of both cylinders is attached below for a better understanding.

<h3>First find the radius of larger cylinder:</h3>

Surface area = 2πrh + 2πr²

236 = 2(3.14)(5)r + 2(3.14)r²

236 = 31.4r + 6.28r²

236 = 6.28(r² + 5r)

35.58 = r² + 5r

r = 3.97 cm

<h3>Find the radius of Smaller cylinder:</h3>

Two cylinders are in proportion if their heights and radius are in proportion:

Ratio of height of small cylinder to big cylinder = 3/5 = 0.6

So ratio of radius of both is also 0.6

Let R be the radius of small cylinder

ratio of radius of small cylinder to big cylinder = R / 3.97

R = (0.6)(3.97)

R = 2.38

<h3 /><h3>Surface Area for small cylinder:</h3>

R = 2.38cm and h = 3 cm

Surface area = 2πrh + 2πr²

Surface area = 2(3.14)(2.38)(3) + 2(3.14)(2.38)²

Surface area = 80.4115cm²

Round of to nearest tenth

Surface area = 80.4 cm²

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Feliz [49]

Answer:

Therefore the mass of the of the oil is 409.59 kg.

Step-by-step explanation:

Let us consider a circular disk. The inner radius of the disk be r and the outer diameter of the disk be (r+Δr).

The area of the disk

=The area of the outer circle - The area of the inner circle

= $\pi (r+\triangle r)^2- \pi r^2$

$=\pi [r^2+2r\triangle r+(\triangle r)^2-r^2]$

$=\pi [2r\triangle r+(\triangle r)^2]$

Since (Δr)² is very small, So it is ignorable.

∴ $A=2\pi r\triangle r$

The density $\delta (r)= \frac{40}{1+r^2}$

We know,

Mass= Area× density

$=(2r \pi \triangle r)(\frac{40}{1+r^2}})$

Total mass $M=\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i$

Therefore

$\sum_{i=1}^n \frac{80r_i\pi }{1+r^2}\triangle r_i=\int_0^5 \frac{80r\pi }{1+r^2}dr$

$=40\pi[ln(1+r^2)]_0^5$

$=40\pi [ln(1+5^2)-ln(1+0^2)]$

$=40\pi ln(26)$

= 409.59 kg (approx)

Therefore the mass of the of the oil is 409.59 kg.

3 0

3 years ago

Write each ratio in simplest fractional form. 1. 16 dogs and 9 cats 2. 99 miles to 6 gallons 3. 4 frogs to 9 lily pads 4. 6 cups

soldi70 [24.7K]

Answer:

1. 16/9

2. 33/2

3. 4/9

4. 3/2

5. 6/13

Step-by-step explanation:

1. 16 dogs and 9 cats

16/9

2. 99 miles to 6 gallons

99/6

Divide by 3 on the top and bottom

33/2

3. 4 frogs to 9 lily pads

4/9

4. 6 cups of milk to 4 cups of flour

6/4

Divide the top and bottom by 2

3/2

5. 6 girls to 13 boys

6/13

6 0

4 years ago

Please help me with this thanks

Kryger [21]

Step-by-step explanation:

B = area of the base

= 9×4 = 36 square inches

P= perimeter of the base

= 2(9+4)

=2×13= 26 inches

H =distance between the bases

= 16 inches

SA= 2B+PH

= 2(36)+ 26× 16

= 72+416 = 488 square inches

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3 years ago

What is a equivalent fraction and decimal to 3 ones and 7 hundreths

nasty-shy [4]

3 ones = 3
7 hundredths = 7/100

So equivalent fraction is 3 7/100 or 307/100.
Equivalent decimal is: 3.07

4 0

3 years ago

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nikitadnepr [17]

7 • 5

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3 years ago