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snow_tiger [21]
3 years ago
7

a solid sphere is cut into 3 equal wedges. the volume of each wedge is V=4/9π^3. solve the formula for r

Mathematics
2 answers:
forsale [732]3 years ago
7 0

Step-by-step explanation:

hmmm.

the other answer says the volume of a wedge is

4/9 × pi×r³

but I read here only

4/9 × pi³

so, what is correct ?

if I assume my reading is correct, then the solution is actually

4/9 × pi×r³ = 4/9 × pi³

pi×r³ = pi³

r³ = pi²

r =  \sqrt[3]{ {\pi}^{2} }

and that would mean

r ≈ 2.145

algol133 years ago
4 0

\\ \qquad\quad\sf{:}\dashrightarrow V=\dfrac{4}{9}πr^3

  • It is one third of the solid. sphere

\\ \qquad\quad\sf{:}\dashrightarrow V_{(Sphere)}

\\ \qquad\quad\sf{:}\dashrightarrow 3\left(\dfrac{4}{9}πr^3\right)

\\ \qquad\quad\sf{:}\dashrightarrow \dfrac{4}{3}\pi r^3

Now

\\ \qquad\quad\sf{:}\dashrightarrow \pi r^3=\dfrac{3V}{4}

\\ \qquad\quad\sf{:}\dashrightarrow r^3=\dfrac{3V}{4\pi}

\\ \qquad\quad\sf{:}\dashrightarrow r=\sqrt[3]{\dfrac{3V}{4\pi}}

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Fine length of BC on the following photo.
MrMuchimi

Answer:

BC=4\sqrt{5}\ units

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

In the right triangle ACD

Find the length side AC

Applying the Pythagorean Theorem

AC^2=AD^2+DC^2

substitute the given values

AC^2=16^2+8^2

AC^2=320

AC=\sqrt{320}\ units

simplify

AC=8\sqrt{5}\ units

step 2

In the right triangle ACD

Find the cosine of angle CAD

cos(\angle CAD)=\frac{AD}{AC}

substitute the given values

cos(\angle CAD)=\frac{16}{8\sqrt{5}}

cos(\angle CAD)=\frac{2}{\sqrt{5}} ----> equation A

step 3

In the right triangle ABC

Find the cosine of angle BAC

cos(\angle BAC)=\frac{AC}{AB}

substitute the given values

cos(\angle BAC)=\frac{8\sqrt{5}}{16+x} ----> equation B

step 4

Find the value of x

In this problem

\angle CAD=\angle BAC ----> is the same angle

so

equate equation A and equation B

\frac{8\sqrt{5}}{16+x}=\frac{2}{\sqrt{5}}

solve for x

Multiply in cross

(8\sqrt{5})(\sqrt{5})=(16+x)(2)\\\\40=32+2x\\\\2x=40-32\\\\2x=8\\\\x=4\ units

DB=4\ units

step 5

Find the length of BC

In the right triangle BCD

Applying the Pythagorean Theorem

BC^2=DC^2+DB^2

substitute the given values

BC^2=8^2+4^2

BC^2=80

BC=\sqrt{80}\ units

simplify

BC=4\sqrt{5}\ units

7 0
2 years ago
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Schach [20]
Right angle (angle p) = 90°
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q = 90°
8 0
3 years ago
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Inessa [10]

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Step-by-step explanation:

∡BAC= 38°

∡BAN= 180°-38° = 142°

7 0
2 years ago
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Idently the graph of f(x) = 3(x - 1) - 4. Then identity the vertex and ads of symmetry find the minimum value of and describe wh
Vesna [10]

Answer:

See below

Step-by-step explanation:

I assume you mean f(x) = 3(x-1)^2-4

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BabaBlast [244]

Answer:

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