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Irina-Kira [14]
3 years ago
11

Find the volume. Help asap. Please.

Mathematics
2 answers:
alexgriva [62]3 years ago
5 0

Use the Pythagorean theorem to find the diameter:

Diameter = √(19.3^2 - 9.5^2)

Diameter = √(372.49 - 90.25)

Diameter = √282.24

Diameter = 16.8 m

Volume of a cylinder = PI x r^2 x h

r = 1/2 diameter = 16.8 /2 = 8.4

h = 9.5 m

Volume = PI x 8.4^2 x 9.5

= PI x 70.56 x 9.5

= PI x 670.32

In terms of PI volume = 670.32PI

As a decimal:

670.32 x 3.14 = 2104.8048 = 2100m^3 ( rounded to the nearest hundred)

Shkiper50 [21]3 years ago
3 0

Hey!

------------------------------------------------

First, we need to find the diameter.

d = √a² - b²

d = √19.3² - 9.5²

d = √372.49 - 90.25

d = √282.24

d = 16.8

Second, find the the radius.

radius = 16.8 / 2

radius = 8.4m.

Third, find the volume.

v = πr²h

v = (3.14)(8.4)²(9.5)

v = (3.14)(70.56)(9.5)

v = 670.32π

v = 2,104.8048...

2,104.8048... ≈ 2,100m.

Answer:

2,100m.

------------------------------------------------

Hope This Helped! Good Luck!

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Answer:

1. m∠R > 90°

2. m∠S + m∠T < 90°

4. m∠R > m∠T

5. m∠R > m∠S

Step-by-step explanation:

<h3>General strategy</h3>
  1. prove the statement starting from known facts, or
  2. disprove the statement by finding a counterexample

Helpful fact:  Recall that the Triangle Sum Theorem states that m∠R + m∠S + m∠T = 180°.

<u>Option 1.  m∠R > 90°</u>

Start with m∠R > m∠S + m∠T.

Adding m∠R to both sides of the inequality...

m∠R + m∠R > m∠R + m∠S + m∠T

There are two things to note here:

  1. The left side of this inequality is 2*m∠R
  2. The right side of the inequality is exactly equal to the Triangle Sum Theorem expression

2* m∠R > 180°

Dividing both sides of the inequality by 2...

m∠R > 90°

So, the first option must be true.

<u>Option 2.  m∠S + m∠T < 90°</u>

Start with m∠R > m∠S + m∠T.

Adding (m∠S + m∠T) to both sides of the inequality...

m∠R + (m∠S + m∠T) >  m∠S + m∠T + (m∠S + m∠T)

There are two things to note here:

  1. The left side of this inequality is exactly equal to the Triangle Sum Theorem expression
  2. The right side of the inequality is 2*(m∠S+m∠T)

Substituting

180° > 2* (m∠S+m∠T)

Dividing both sides of the inequality by 2...

90° > m∠S+m∠T

So, the second option must be true.

<u>Option 3.  m∠S = m∠T</u>

Not necessarily.  While m∠S could equal m∠T, it doesn't have to.  

Example 1:  m∠S = m∠T = 10°;  By the triangle sum Theorem, m∠R = 160°, and the angles satisfy the original inequality.

Example 2:  m∠S = 15°, and m∠T = 10°;  By the triangle sum Theorem, m∠R = 155°, and the angles still satisfy the original inequality.

So, option 3 does NOT have to be true.

<u>Option 4.  m∠R > m∠T</u>

Start with the fact that ∠S is an angle of a triangle, so m∠S cannot be zero or negative, and thus m∠S > 0.

Add m∠T to both sides.

(m∠S) + m∠T > (0) + m∠T

m∠S + m∠T > m∠T

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠T.

So, option 4 must be true.

<u>Option 5.  m∠R > m∠S</u>

Start with the fact that ∠T is an angle of a triangle, so m∠T cannot be zero or negative, and thus m∠T > 0.

Add m∠S to both sides.

m∠S + (m∠T) > m∠S + (0)

m∠S + m∠T > m∠S

Recall that m∠R > m∠S + m∠T.

By the transitive property of inequalities, m∠R > m∠S.

So, option 5 must be true.

<u>Option 6.  m∠S > m∠T</u>

Not necessarily.  While m∠S could be greater than m∠T, it doesn't have to be.  (See examples 1 and 2 from option 3.)

So, option 6 does NOT have to be true.

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