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Yuliya22 [10]
3 years ago
11

A frustum is made by removing a small cone from a similar large cone in the diagram shown the height of a small cone is a quarte

r of the height of the large chrome work out the volume of the frustum

Mathematics
1 answer:
lesantik [10]3 years ago
6 0

Answer:

Volume of the frustum = ⅓πh(4R² - r²)

Step-by-step explanation:

We are to determine the volume of the frustum.

Find attached the diagram obtained from the given information.

Let height of small cone = h

height of the large cone = H

The height of a small cone is a quarter of the height of the large cone:

h = ¼×H

H = 4h

Volume of the frustum = volume of the large cone - volume of small cone

volume of the large cone = ⅓πR²H

= ⅓πR²(4h) = 4/3 ×π×R²h

volume of small cone = ⅓πr²h

Volume of the frustum = 4/3 ×π×R²h -  ⅓πr²h

Volume of the frustum = ⅓(4π×R²h - πr²h)

Volume of the frustum = ⅓πh(4R² - r²)

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Can anyone help me?
ArbitrLikvidat [17]

Answer:

The factored form of 4<em>m</em>³ – 28<em>m</em>² – 120<em>m</em> is 4<em>m</em>(<em>m</em> – 10)(<em>m</em> + 3). The zeroes of the function would be <em>m</em> = 0, <em>m</em> = –3, and <em>m</em> = 10.

Step-by-step explanation:

I'll give this a shot.

4<em>m</em>³ – 28<em>m</em>² – 120<em>m</em> = 0 — The original expression

4<em>m</em>³ – 28<em>m</em>² – 120<em>m</em> — Did that 0 have any purpose? I just deleted it.

4(<em>m</em>³ – 7<em>m</em>² – 30<em>m</em>) — There's a common factor in here, 4. Let's pull that aside.

4m(<em>m²</em> – 7<em>m</em> – 30) — Actually, there's <em>two</em> common factors. The second one is <em>m</em>! Let's pull <em>that</em> out too!

To factor an expression, you have to break apart the middle term, so to speak. That's only possible if you can find two numbers whose product equals that of the outside terms and whose sum equals the middle term. Here, I'm just dealing with numbers and putting that variable aside.

–30 = 10 × –3

–30 = –10 × 3

–30 = –2 × 15

–30 = 2 × –15 — To solve for any potential factors, let's find all the numbers integers that multiply to –30

Now let's see which one adds up to –7!

15 – 2 = 13 — it's not this one

2 – 15 = –13 — nor this one

10 – 3 = 7 — we're pretty close! Let's switch that negative

3 – 10 = –7 — here we go! Here's our numbers!

4<em>m</em>[(<em>m</em>² – 10<em>m</em>) + (3<em>m</em> – 30)] — now we break apart the middle term. This is <em>all</em> multiplied by 4<em>m</em>, so that still encases everything with brackets.

4<em>m</em>[<em>m</em>(<em>m</em> – 10) + 3(<em>m</em> – 10)] — Factoring the two expressions

4<em>m</em>(<em>m</em> + 3)(<em>m</em> – 10) — simplifying to find our answer! Ta-da!

8 0
3 years ago
Factor completely 2x3 + 8x2 + 3x + 12.
goblinko [34]

Answer:

(2x^2+3)(x+4).

Step-by-step explanation:

2x^3+8x^2+3x+12

We need to find the factors of given equation;

Solution:

On Solving the above equation we get;

Now First we will take common factor from first 2 terms which is 2x^2 we get;

2x^2(x+4) + 3x+12

Now we will take the common factor from the last 2 terms which is 3 we get;

2x^2(x+4) + 3(x+4)

Here we get 2 terms in which (x+4) is common factor.

(x+4)(2x^2+3)

Hence After factorizing the given equation we get (2x^2+3)(x+4).

8 0
3 years ago
1) if side C of a right triangle is 12 and side B of a right triangle is 8 what does side A equal​
GarryVolchara [31]
The answer is 4 square root 5 or -4 square root 5

3 0
3 years ago
Can u guys PLEASE explain the difference between 2 x 10 to the power of 4 and 2 to the power of 4
Alexxx [7]

Answer:

see explanation

Step-by-step explanation:

2 × 10^{4}

= 2 × 10 × 10 × 10 × 10

= 2 × 100 × 100

= 200 × 100

= 20000

And

2^{4}

= 2 × 2 × 2 × 2

= 4 × 4

= 16

7 0
3 years ago
F(1)=3f(1)=3 and f(n)=2f(n-1)+3 <br><br> f(n)=2f(n−1)+3 <br><br> then find the value of f(3)
gayaneshka [121]

Answer:

f(3)=21

Step-by-step explanation:

f(1)=3

f(n)=2f(n-1)+3

n=2

f(2)=2f(2-1)+3

f(2)=2f(1)+3

f(2)=2*3+3

f(2)=6+3

f(2)=9

n=3

f(3)=2f(3-1)+3

f(3)=2f(2)+3

f(3)=2*9+3

f(3)=18+3

f(3)=21

7 0
3 years ago
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