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Gemiola [76]
2 years ago
10

I) find, in terms of π, the curved surface area of a cone with circular base diameter 10cm and height 12cm.

Mathematics
2 answers:
iris [78.8K]2 years ago
4 0

Answer:

\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}

( i )

  • given - a cylinder with base diameter = 10 cm ! And , height = 12 cm

  • To find - CSA of cone

now ,

since diameter = 10 cm

\implies \: radius =  \frac{10}{2}  = 5 \: cm \\

now ,

slant \: height \: ( \: l \: ) =  \sqrt{h {}^{2}  + r { }^{2} }  \\  \\ \implies \:  \sqrt{(12) {}^{2} + (5) {}^{2}  }  \\  \\ \implies \:  \sqrt{144 + 25}  \\  \\ \implies \:  \sqrt{169}  \\  \\ \implies \: 13 \: cm

now ,

CSA \: of \: cone = \pi \:  \times r \times l \\  \\ \implies \: \pi \:  \times 5 \times 13 \\  \\ \implies \: 65\pi \: cm {}^{2}

_____________________________

_____________________________

( ii )

now when we flatten the cone ,

the slant height becomes the radius of the sector , while the arc becomes the circumference of cone !

\therefore \: radius = l = 13 \: cm \\  \\ arc \: length = circumference = 2\pi  \: r

now ,

s = d \: \theta \: ( \: for \: a \: sector \: ) \\  \\ \therefore \: l\theta \:  = 2\pi \: r \\  \\ \implies \: \theta =  \frac{2\pi \: r}{l}  \\  \\ \implies \: \theta =  \frac{2 \times \pi \times 5}{13}  \\   \\ \implies \: \theta \:  =  \frac{10\pi}{13} \\ \\ \implies \theta \: = \: 0.77 \pi

hope helpful :D

Paraphin [41]2 years ago
3 0

Step-by-step explanation:

i)

remember, the radius is half the diameter !

the overall surface area of a cone (base circle + "mantle", the lateral, curved surface) is

A = pi×r × (r + sqrt(h² + r²))

so, only the "mantle" or lateral curved stave area is

pi×r × sqrt(h² + r²) = pi×5 × sqrt(12² + 5²) = pi×5×sqrt(169) =

= pi×5×13 = 65×pi cm²

ii)

the length of the arc of the sector is the circumference of the circle, that was the base of the original cone.

that is

2×pi×r = 2×pi×5 = 10×pi cm

the total circumference of the large circle containing that sector is

2×pi×r' = 2×pi×sqrt(h² + r²)

as the radius r' of the circle containing the sector (representing the "mantle" of the cone) is the lateral height of the cone (the distance along its side from the base to the top). and that is per Pythagoras simply the square root of the sum of the square of the inner height and the square of the base radius.

in our case that is

2×pi×sqrt(12² + 5²) = 2×pi×13 = 26×pi cm

the angle of the sector is then 10/26 of the total of 360° for the whole circle :

360 × 10/26 = 138.4615385...°

or, if you need this in terms of pi too, remember that 360° are represented by 2×pi (the arc length of the standard circle).

2×pi × 10/26 = pi × 20/26 = pi × 10/13 =

= 0.769230769... × pi

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Answer:

2.0 x 10^11

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3 years ago
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3 0
3 years ago
What additional information do you need to prove triangle NOP = triangle QSR?
Wewaii [24]
After careful consideration i think I have an answer... 
So if you notice, These two triangles are a reflection of each other. 
Now even though these two triangles equal one another, we still have to consider the fact that they are different. (one side is the opposite of another)
So lets just name all the sides that equal each other. 
∠N = ∠Q
NO = QS
QR = NP
PO = SR
∠S = ∠O 
∠P = ∠R 

(by the way i'm going to be saying {the reflective side} every time i want to refer to the side with the two lines :P) - so bare with me. 

So therefore this would mean that ∠P = ∠S would be false, since one angle is from the side that is reflected and the other isn't. Makes sense?

So lets look over at the answers...

A.) PN = SQ 
For this answer choice, PN is on the non reflective side, while SQ is on the reflective side. Soooo... This answer choice is wrong. 

B.) NO = QR
NO  is part of the  unreflective side, while QR is part of the reflective side. 
Therefore this answer is wrong. They must be part of the same side. 

C.) ∠P = ∠S 
∠P is on the unreflective side, while angle ∠S is on the reflective side. 
There fore this answer is also wrong. 

D.) ∠O = ∠S 
Now ∠O is on the reflective side while ∠S is on the reflective as well. 
There fore this answer is correct . 

YOUR ANSWER IS. 
D.) ∠O = ∠S 

Good Luck! :)


6 0
3 years ago
A.It will stay the same
DanielleElmas [232]

Answer:

B

Step-by-step explanation:

Let's arrange the data set in increasing order.

We have 19, 27, 27, 33, 45, 53. The median is (27 + 33) / 2 = 30.

The new set is 19, 27, 27, 33, 45, 53, 90. The new median is 33.

Since 33 - 30 = 3 the answer is B.

4 0
3 years ago
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