Question

The volume of a cone is three hundred cubic kilometers. If the radius of the base is 9 kilometers, what is the height of the cone? Use three point one four for pi. Show your work and round to the nearest tenth.

Answer 1

volume of a cone = \(\frac{1}{3} \pi r^2 h\)

where do you have troubles?

Answer 2

i cant find the height

Answer 3

okay...start by identifying the values given to you...which of those are given?

Answer 4

the overall volume wich is 300 cubic km and the radius wich is 9 km

Answer 5

good! and it says that pi is 3.14 so we substitute... \[300 = \frac{1}{3} (3.14)(9)^2h\]

good?

Answer 6

yah

Answer 7

1/3 x 3.14 x 81 x h = 300 cubic km

Answer 8

now how should i find the height

Answer 9

good \[300 = \frac{1}{3} (3.14) (81) h\] first we multiply both sides by 3 to get rid of 1/3

Answer 10

ok so that would be 9.42 x 243?

Answer 11

no no no...if we multiply the right side by 3...then 1/3 just cancels out okay?

Answer 12

\[\frac{1}{3} \times 3 = 1\]

Answer 13

i did not get that...

Answer 14

\[\frac{1}{3} (3.14)(81) h \times 3 = \frac{3}{3} (3.14)(81) h\] how about that?

Answer 15

ok so i multiply 1/3 by 3 not anyting else?

Answer 16

nothing else on the right side..you multiply 3 to 300 as well

Answer 17

i still dont understand well im sorry

Answer 18

according to multiplicative property of equality..you need to multiply BOTH sides by THE SAME number

\[300 = \frac{1}{3} (3.14)(81) h \rightarrow 300(3) = \frac{3}{3} (3.14)(81)h\] okay?

Answer 19

i just multiply BOTH sides by 3

Answer 20

ok

Answer 21

so what's 300 x 3?

Answer 22

900

Answer 23

good and what's \(\large \frac{3}{3}\)

Answer 24

it is 3

Answer 25

it's not 3...that's like 3 divided by 3

Answer 26

a number divided by itself...

Answer 27

then its 0 ?

Answer 28

no sorry
its 1

Answer 29

final answer /:)

Answer 30

so my height is 1?

Answer 31

no...im asking if you're sure that \(\large \frac{3}{3} = 1\)

Answer 32

yes

Answer 33

then it becomes \[900 = (3.14)(81) h\] agree?

Answer 34

yes

Answer 35

so what's \(3.14 \times 81?\)

Hint: use a calculator

Answer 36

254.34

Answer 37

good..now we divide both sides by 254.34 \[\large \frac{900}{254.34} = \frac{(\cancel{254.34})h}{\cancel{254.34}}\]

Answer 38

ok

Answer 39

A 9 kilometer radius of the base. A huge cone. Seriously, people who make textbooks don't ever think for real.

Answer 40

3.53857042

Answer 41

there we go!

Answer 42

Round to the nearest tenths @mumina1999

Answer 43

dont forget units ;D

Answer 44

ok
thanks guys