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yKpoI14uk [10]
2 years ago
8

What is the surface area of a sphere with a radius of 12 units?

Mathematics
1 answer:
dexar [7]2 years ago
5 0

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

\blue\textsf{\textbf{\underline{\underline{Question:-}}}}

What is the volume of a sphere with a radius of 12 units?

\blue\textsf{\textbf{\underline{\underline{Answer and How to Solve:-}}}}

\sf{Formula \ for \ Volume \ of \ a \ sphere \ : \bigstar\boxed{\bold{V=\displaystyle\frac{4}{3} \pi r^3}}

Where

\tt{V=Volume}\\\tt{\pi =pi}\\\tt{r=radius}

Provided Information:-

\tt{r=12\:units}

Plug in:-

\bold{V=\displaystyle\frac{4}{3} \pi (12)^3}

\bold{V=\displaystyle\frac{4}{3} \pi (1,728)}

On further simplification,

\dashrightarrow\boxed{\boxed{\underline{\bold{V=2304\pi\:m^3}}}}\dashleftarrow

<h3>Good luck.</h3>

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

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ZA and ZB are complementary angles. If mZA = (7x + 23)° and
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Answer:

ZB= 39°

Step-by-step explanation:

complementary angles are angles that add up to equal 90

equation:  7x + 23 + 5x + 19 = 90

add like terms: 12x + 42 = 90

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Can someone help me with this please
Bingel [31]

Answer:

  A.1: ∠BAC ≅ ∠BDC ≅ ∠EDF, ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF

  A.2: ∠1 ≅ ∠4, ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6

  A.3: ∠2 ≅ ∠3

  B.1: ∠ACD ≅ ∠CAB, ∠CDA ≅ ∠ABC, ∠DAC ≅ ∠BCA

  B.2: ∠1 ≅ ∠3 ≅ ∠5, ∠2 ≅ ∠4 ≅ ∠6

  see "additional comment" regarding listing pairs

Step-by-step explanation:

There are a number of ways angles can be identified as congruent. In each case, the converse of the proposition is also true.

  • opposite angles of a parallelogram are congruent
  • corresponding angles where a transversal crosses parallel lines are congruent
  • alternate interior angles where a transversal crosses parallel lines are congruent
  • vertical angles are congruent
  • any two angles with the same measure are congruent

In these exercises, pairs of angles need to be examined to see which of these relations may apply.

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<h3>A</h3>

<u>Left</u>

ABCD is a parallelogram, so the congruent angles are opposite angles and any that are vertical or corresponding:

  ∠BAC ≅ ∠BDC ≅ ∠EDF ≅ 110° (3 pairs)

  ∠ACD ≅ ∠ABD ≅ ∠BDE ≅ ∠CDF ≅ 70° (6 pairs)

<u>Center</u>

  ∠1 ≅ ∠4 ≅ 66° (1 pair) . . . . vertical angles

  ∠2 ≅ ∠3 ≅ ∠5 ≅ ∠6 ≅ 57° (6 pairs) . . . . marked with the same measure, and their vertical angles

<u>Right</u>

Assuming that lines appearing to go in the same direction actually do go in the same direction, the only pair of congruent angles in the figure is ...

  ∠2 ≅ ∠3

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<h3>B</h3>

<u>Left</u>

Corresponding angles in congruent triangles are congruent. Here, the congruent triangles are ΔACD ≅ ΔCAB. So, the pairs of congruent angles are ...

  ∠ACD ≅ ∠CAB (30°)

  ∠CDA ≅ ∠ABC (90°)

  ∠DAC ≅ ∠BCA (60°)

<u>Right</u>

The corresponding angles and any vertical angles are congruent. This means all the odd-numbered angles in the figure are congruent, and all the even-numbered angles in the figure are congruent. The marked 72° angles show the "horizontal" segments are parallel by the converse of the corresponding angles theorem.

  ∠1 ≅ ∠3 ≅ ∠5 (72°) (3 pairs)

  ∠2 ≅ ∠4 ≅ ∠6 (108°) (3 pairs)

_____

<em>Additional comment</em>

The question asks you to list pairs of congruent angles. When 3 things are congruent, they can be arranged in 3 pairs:

  a ≅ b ≅ c   ⇒   (a≅b), (a≅c), (b≅c)

Similarly, when 4 things are congruent, they can be arranged in 6 pairs:

  a ≅ b ≅ c ≅ d   ⇒   (a≅b), (a≅c), (a≅d), (b≅c), (b≅d), (c≅d)

In the above, we have elected not to list all of the pairs, but to list the set of congruences from which pairs can be chosen.

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Read 2 more answers
Cylinder A has a radius of 1 m and a height of 4 m. Cylinder B has a radius of 2 m and a height of 4 m. What is the ratio of the
Svetlanka [38]

Note: The volume of a cylinder is:

radius² × π × height

First lets work out the volume of Cylinder A:

Volume = 1² × π × 4

             = 4π  m³

Now lets work out the volume of Cylinder B

Volume = 2² × π × 4

             = 16π  m³

__________________________________________

Now lets compare the volumes ( Cylinder A : Cylinder B)  :

4π : 16π

Lets simplify this by dividing both sides by 4π:

     4π : 16π            <em>( </em>÷ <em>4π)</em>

----> 1 : 4        

_____________________________________________________

Answer:

Option b) 1 : 4

8 0
3 years ago
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