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Arte-miy333 [17]
4 years ago
7

Calculate the surface area and the volume of the cylinder.

Mathematics
1 answer:
algol134 years ago
4 0

Step-by-step explanation:

Surface area of a cylinder:

A = (2 x pi x r x h) + (2 x pi x r^2)

(2 x pi x 5 x 25) + (2 x pi x 5^2)

785.3981 + 157.0796 = 942.4777cm^2

Volume of cylinder:

V = pi x r^2 x h

pi x 5^2 x 25 = 1963.4954cm^3

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A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021
egoroff_w [7]

The sum of the given series can be found by simplification of the number

of terms in the series.

  • A is approximately <u>2020.022</u>

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

  • \displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

  • \displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}

Therefore, for the last term we have;

  • \displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

\displaystyle \frac{A}{2}  = \mathbf{ 1011 \cdot  \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460}  \right)}

\displaystyle \frac{A}{2}  = 1011 \cdot  \left(1 - \frac{1}{2} +\frac{1}{2} -  \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022}  \right)

Which gives;

\displaystyle \frac{A}{2}  = 1011 \cdot  \left(1 - \frac{1}{2022}  \right)

\displaystyle  A = 2 \times 1011 \cdot  \left(1 - \frac{1}{2022}  \right) = \frac{1032231}{511} \approx \mathbf{2020.022}

  • A ≈ <u>2020.022</u>

Learn more about the sum of a series here:

brainly.com/question/190295

8 0
2 years ago
Read 2 more answers
Emily is entering a bicycle race for charity. Her mother pledges $0.40 for every 0.75 miles she bikes. If Emily bikes 21 miles,
lora16 [44]

Answer:

Her mother will donate $11.20

Step-by-step explanation:

  • $0.40 every 0.75 miles.
  • 21 miles biked.

Step 1: Figure out how many 0.75 increments are in 21 miles.

21 ÷ 0.75 = 28

  • There are 28 increments of 0.75 in 21 miles.

Step 2: Multiply 28 by $0.40

28 * $0.40 = $11.20

4 0
3 years ago
Read 2 more answers
Please help quickly !!
Ira Lisetskai [31]

Answer:

I believe you have to add 15.9 on both sides

4 0
3 years ago
If F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30 find each measure
seraphim [82]

Answer:

The measure of JK is 60

Step-by-step explanation:

It is given that the points F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30.

The point F is midpoint of JK, point G is midpoint of KL and the point H is midpoint of LJ as shown in figure .

According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third si

8 0
3 years ago
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PLEASE PLEASE PLEASE HELP FAST!!!!!!!!!! WILL REPORT ANY TROLLS
worty [1.4K]

Answer:

i think its 1.5 im not sure tho 1.5 sounds the best

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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