Question

Suppose that a sphere with radius 5a has the same volume as a cone of radius 3a. What is the height of the cone? Give your answer in terms of a. Use the formulas and for the volumes of a sphere and cone respectively.

Answer 1

heres the formulas
sphere=v=3/3pier^3
cone=v=1/3pier^2

Answer 2

\[\Large \frac 43 \pi \left( 5a \right)^3=\frac 13 \pi \left( 3a \right)^2h\]
solve for h

Answer 3

how do i figure out how to solve it?

Answer 4

use just the algebra inverse operation steps....you want the h remaining alone on the right hand side, so first I would multiply each side by the reciprocal of 1/3, that being a 3/1 .....

Answer 5

write that down and follow me as I go...

Answer 6

ok

Answer 7

so that would look like...\[3/1 * 4/3\Pi ^{}\]

Answer 8

darn, where's the rest I typed!! \[(5a)^{3} = \Pi (3a)^{2}h\]

Answer 9

is that last symbol pie

Answer 10

yes, believe it or not! not a good choice..maybe its really the Roman numeral for 2! anyway pi...:-)

Answer 11

ok, so simplify and on the left, the 3's cancel out when you cross cancel in that fraction, leaving you with just a 4 pi ( )^3 = pi ( ) ^2 h

Answer 12

now just divide both sides by pi, and they will completely cancel out....leaving you with jsut the 4(5a)^3 = (3a)^2 h

Answer 13

Now a couple of ways to go....I'll do the long way so you can understand what I do without me skipping any steps...

Answer 14

ok thank you

Answer 15

Simplify each side before you do any more inverse operations (this actually could have been your very first step)....you get 4 * 125a^3 = 9a^2*h see where this all came from?

Answer 16

so far yes

Answer 17

ok, now keep simplifying,,,LS will = 1000a^3 = 9a^2 h

Answer 18

now divide both sides by 9^2....you get (1000a^3)/(9a^2) = h

Answer 19

simplify another time, to get 1000a/9 = h.....do you have a multiple choice?

Answer 20

yes i do

Answer 21

is that one of them?? I hope! :-)

Answer 22

no there is 500 on top the fraction

Answer 23

but the 9's there?

Answer 24

yes

Answer 25

oh! mis-multiplied! that's what I get for doing all this in my head....4* 125 is 500, not 100. :-)

Answer 26

not 1000

Answer 27

nope

Answer 28

Have any others similar to this?

Answer 29

i got 500a over 9 and 9 over 500a

Answer 30

500a/9 is the correct answer......you could also simplify the ( ) 1st, then cross cancel on each side with the fractions you have, first the one on the left then the one on the right....

Answer 31

thank you for your help

Answer 32

you're welcome!