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worty [1.4K]
3 years ago
11

Cone A has a radius 12 inches and Cone B has a radius of 30 inches. If the cones are similar and the volume of Cone A if 48, fin

d the volume of Cone B.
Mathematics
2 answers:
ziro4ka [17]3 years ago
6 0

Answer:

  750 cubic inches

Step-by-step explanation:

The ratio of linear dimensions is ...

  (radius B)/(radius A) = (30 in)/(12 in) = 2.5

Then the ratio of volumes is

  (volume B)/(volume A) = (2.5)^3 = 15.625

So, ...

  volume B = (volume A)·15.625 = 750 . . . . cubic inches

The volume of Cone B is 750 cubic inches.

_____

The ratio of volumes is the cube of the ratio of linear dimensions (radius) when the figures are similar.

If the volume of Cone A is ...

  V = (π/3)r^2h

and the ratio of dimensions is k, then the volume of Cone B is ...

  V = (π/3)(kr)^2(kh) = (π/3)r^2h(k^3) . . . . k^3 times the volume of Cone A

Ilia_Sergeevich [38]3 years ago
4 0

Answer:

750 cubic inches.....

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Financial literacy is important because it equips us with the knowledge and skills we need to manage money effectively. Without it

Step-by-step explanation:

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2 years ago
Solve this Inequality 1 &gt; -1 - w
Rom4ik [11]

Answer:

\displaystyle -2 < w

Step-by-step explanation:

1 > −1 - w

+ 1 + 1

________

\displaystyle \frac{2}{-1} > \frac{-w}{-1} \\ \\ -2 < w

Whenever you divide\multiply by a <em>negative</em>, you reverse the inequality symbol.

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2 years ago
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AfilCa [17]

Answer:

16

Step-by-step explanation:

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5 0
3 years ago
Help me with these questions
Elena L [17]

Answer: a = 4, b = 163,422

<u>Step-by-step explanation:</u>

P = P_{0} e^{kt}   P is the new population, P₀ is the initial population, k is the growth rate, t is the time elapsed.

Part a) What do we know?

P = 7003

P₀ = unknown

k = .21 <em>(converted 21% into a decimal)</em>

t = 36 yrs <em>(2006 - 1970) </em>

P = P_{0} e^{kt}   <em>need to solve for P₀</em>

7003 = P_{0} e^{(.21)(36)}

7003 = P_{0} e^{7.56}

7003 = P₀ (1920)

\frac{7003}{1920} = P_{0}

3.6 = P₀

rounded to the nearest whole number = 4

Part b) What do we know?

P = unknown

P₀ = 7003

k = .21 <em>(converted 21% into a decimal)</em>

t = 15 yrs <em>(2021 - 2006) </em>

P = P_{0} e^{kt}   <em>need to solve for P₀</em>

P = 7003 e^{(.21)(15)}

P = 7003 e^{3.15}

P = 7003(23.33)

P = 163,422.46

rounded to the nearest whole number = 163,422

*************************************************************

Answer: 2, -1

<u>Step-by-step explanation:</u>

eˣ² = eˣ * e²

eˣ² = eˣ⁺²

x² = x + 2

x² - x - 2 = 0

(x - 2)(x + 1) = 0

x - 2 = 0      or      x + 1 = 0

 x = 2          or         x = -1

Check both answer for validity:

eˣ² = eˣ⁺²

e⁴ = e⁴     or   e¹ = e¹

TRUE             TRUE

*****************************************

Answer: 0 = ln 1

<u>Step-by-step explanation:</u>

e^{-10} = \frac{1}{e^{10}}

ln(e^{-10}) = ln(\frac{1}{e^{10}})

-10 = ln 1 - 10   <em>log rules say division is subtraction</em>

 0 = ln 1



5 0
3 years ago
I need help what is the answer plz
dlinn [17]

Answer:

-2.25

Step-by-step explanation:

Since there are 4 ticks between 2 numbers, we do 1/4 = 0.25

Now we find the value:

-2.25

8 0
3 years ago
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