Question

A right circular cone has a lateral area of 1,280 pi ft^2 and a base area of 512pi ft^2 . Find the volume.

Answer 1

@amistre64 @SolomonZelman

Answer 2

@phi

Answer 3

do you know the formula for
1) lateral area
2) base area (area of a circle)
3) volume of a cone

can you write down those 3 formulas?

Answer 4

i always have to reinvent the lateral formula .... never sticks in my memory

Answer 5

LA= pi*r*l
V= 1/3*pi*r^2*h
base= pi*r^2

Answer 6

next, look at what we are given.
base area of 512pi
any ideas how to use that to find one of things we need to know to use the V formula?

Answer 7

the radius?

Answer 8

ok, sounds good.
I would use
\[ \pi r^2 = 512 \pi\]
what do you get for r ?

Answer 9

first divide both sides by pi

Answer 10

sqroot of 512

Answer 11

or 22.6

Answer 12

I would leave things exact until the very end. so sqrt(512)
you can write that as sqrt(2*256) and everybody knows 16*16 = 256 (kidding)
so you can write r= 16 * sqr(2)
or just keep it sqr(512)

Answer 13

the radius again?

Answer 14

if you know the radius (and you do) you put that on your list of "known"
look at the formula:
LA = pi * r * L
which of those "letters" do we know? (btw , we know pi)

Answer 15

la, pi, and r so it must be L?

Answer 16

yes. You always try to get only 1 "unknown" letter. then you can "solve for it"

Answer 17

can you solve for L (L is the slant height of the cone) ?

Answer 18

do you need help solving for L ?

Answer 19

I got 56.64

Answer 20

h and L are different?

Answer 21

let's see
pi * r * L= 1280
r is sqr(512)
\[ L= \frac{1280}{\pi \cdot \sqrt{512} } \]
is that what you did to find L ?

Answer 22

the pi will cancel

Answer 23

oh, I did not see it was 1280 pi

Answer 24

cuz the given is 1280 pi ft^2

Answer 25

yup, 56.64 is what i got

Answer 26

ok, I hope you are keeping track of these numbers. btw, if you use decimals, try to keep more decimals so you get a reasonably accurate answer.

Answer 27

ok

Answer 28

next, we look at the formula for volume of a cone
V= 1/3*pi*r^2*h
we know 1/3
the pi r^2 (notice this!) is the area of the base, and that is 512 pi
we need h

Answer 29

yup, how can we find h?

Answer 30

Here is a picture
http://www.web-formulas.com/math_formulas/geometry_surface_of_cone.aspx

Answer 31

do you see h, r and l form a right triangle ?
any thoughts?

Answer 32

i got 52 as the h

Answer 33

how?

Answer 34

h^2= L^2-r^2

Answer 35

by PT

Answer 36

ok, but keep more decimals

Answer 37

i got a large number of it, i got 27798.96427

Answer 38

is it right?

Answer 39

write down the formula
\[ V= \frac{1}{3} \pi r^2 h \]
the pi r^2 is 512 pi (right?)
h is 51.8459
so
\[ V= \frac{1}{3} \pi \cdot 512 \cdot 51.8459 \]
you need to multiply that out using a calculator.

Answer 40

I get 27797.978
rounded to the nearest whole number 27,798

Answer 41

yup i got a calculator here

Answer 42

ok but you got 27798.96427 which rounds to 27799 (one too large?) typo?

Answer 43

ok i will just use your answer

Answer 44

it's not too hard to redo the multiplies, is it ?

Answer 45

2 more problems here can you help me?

Answer 46

maybe one more if you are quick?

Answer 47

please make it a new post