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3 years ago

The radius AND height of a cylinder are each doubled. What is the new volume?

Mathematics

1 answer:

Naya [18.7K]3 years ago

7 0

The volume of a cylinder is given by

$V = \pi hr^2$

Let $h\mapsto 2h$ and $r\mapsto 2r$

The new volume becomes

$V = \pi(2h)(2r)^2 = \pi\cdot 2h \cdot 4r^2 = 8\pi hr^2$

So, the new volume is 8 times the original volume. In fact, volume scales linearly with the height and quadratically with the radius.

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3 years ago

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2 years ago

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HELP ASAP ITS SO HARD! Kelsey did the following division problem. Her teacher says that the quotient she found is wrong. −2 5/6

SpyIntel [72]

Part A

Her steps were

$-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{6}{17} \times \frac{3}{4}\\\\-\frac{6\times 3}{17\times4}\\\\-\frac{18}{68}\\\\-\frac{9}{34}\\\\$

Kelsey made a mistake on line 3. Note how the 17/6 flips to 6/17. This is not correct. You keep the first fraction the same, but you do flip the second fraction. This only applies when you divide two fractions.

The third step should look like $-\frac{17}{6}\times \frac{3}{4}$

=======================================================

Part B

Here's what she should have written

$-2 \frac{5}{6} \div 1 \frac{1}{3}\\\\-\frac{17}{6} \div \frac{4}{3}\\\\-\frac{17}{6} \times \frac{3}{4}\\\\-\frac{17\times 3}{6\times 4}\\\\-\frac{51}{24}\\\\-\frac{17}{8}\\\\$

If you want to convert that improper fraction to a mixed number, then you could do something like this

$-\frac{17}{8} = -\frac{16+1}{8}\\\\-\frac{17}{8} = -\frac{16}{8}-\frac{1}{8}\\\\-\frac{17}{8} = -2 \frac{1}{8}\\\\$

Or you could divide 17 over 8 using long division to get 2 remainder 1. The 2 is the quotient that goes to the left of the 1/8. The remainder of 1 is the numerator of 1/8.

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