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bulgar [2K]
2 years ago
11

A cone of volume 54π is cut by a plane parallel to the base, 1/3 of the way up the height of the cone (from the base). Find the

volume of the resulting frustum.
Mathematics
1 answer:
Sophie [7]2 years ago
7 0

Answer:

Correct answer:  Vf = 38 π

Step-by-step explanation:

Given:

Vc = 54 π

The ratio of the height of the cone and the height of the frustum is:

Hc : Hf = 3 : 1  ⇒ Hc = 3 · Hf

The ratio of the radius R of the base of the cone to the radius r of the upper base of the frustum is:

R : r = Hc : (Hc - Hf)  ⇒ R : r = (3· Hf) : (3 · Hf - Hf) ⇒ R : r = 3 · Hf : 2 · Hf

R : r = 3 : 2 ⇒  r = (2/3) · R

The formula for calculating the volume of a cone is:

Vc = (R² · π · Hc) / 3 = (R² · π · 3 · Hf) / 3 = R² · π · Hf

The formula for calculating the volume of a frustum is:

Vf = (π · Hf · (R² + R · r + r²)) / 3 = (π · Hf · (R² + R · (2/3) · R + ((2/3) R)²)) / 3

Vf = (π · Hf · (R² + (2/3) ·R² + (4/9) · R²)) / 3 ⇒

Vf = (π · Hf · ( (9/9)R² + (6/9) ·R² + (4/9) · R²)) / 3 ⇒

Vf = (π · Hf · (19/9) · R²) / 3 = (19/27) · R² · π · Hf

Vc / Vf = (R² · π · Hf) / ((19/27) · R² · π · Hf)

R², π and Hf were shortened and we get:

Vc / Vf = 27 / 19  ⇒  Vf = (19 · Vc) / 27 ⇒

Vf = 19 · 54 · π / 27 = 38 π

Vf = 38 π

God is with you!!!

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Dafna1 [17]

Answer:

To spend at most $93, they need to rent the room less than or equal 13 hours.

Step-by-step explanation:

<u><em>The complete question is</em></u>

To rent a certain meeting room, a college charges a reservation fee of $15 and an additional fee of $6 per hour. The chemistry club wants to spend at most $93 on renting a room. What are the possible numbers of hours the chemistry club could rent the meeting room? Use t for the number of hours. Write your answer as an inequality solved for t,

Let

t ----> the number of hours

we know that

I this problem the word "at most" means "less than or equal to"

The number of hours rented multiplied by the cost per hour, plus the reservation fee, must be less than or equal to $93

so

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solve for t

subtract 15 both sides

6t\leq 93-15

6t\leq 78

Divide by 6 both sides

t\leq 13\ hours

therefore

To spend at most $93, they need to rent the room less than or equal 13 hours.

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3 years ago
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wariber [46]

Answer:

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Westkost [7]

Answer:

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Step-by-step explanation:

Factor the polynomial.

3 0
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