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3 years ago

What is the height of cone S?

Mathematics

2 answers:

ale4655 [162]3 years ago

7 0

(Set up a proportion: 768pi/6144pi = x/24)
(Cross multiply: 6144pi*x = 18432pi)
(Divide both sides by 6144pi: x = 3)
(The height of cone S = 3 cm)

balu736 [363]3 years ago

4 0

Answer:

12 cm

Step-by-step explanation:

First, we find the scale factor from cone S to cone T.

ratio of volumes = (vol of T)/(vol of S) = (6144 pi cm^3)/(768 pi cm^3) = 8

The ratio of the volumes is 8:1

The scale factor, which is the ratio of linear dimensions (height, radius, etc.), is the cubic root of the ratio of the volumes.

scale factor = cubic root of 8 = 2

The height of cube T is 24 cm, so the height of cube S is 24 cm/2 = 12 cm.

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Summation notation of the given series

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$\displaystyle \large{\sum_{k=1}^n a_k}$

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Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

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Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

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<u>Arithmetic Sequence</u>

$\displaystyle \large{a_n=a_1+(n-1)d}$

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So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

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