Question

Find the volume of the cone ...



if the heights of the solids are equal and the cross sectional areas at every level parallel to the respective bases are also equal.

Answer 1

Do you know the formula for the volume of a pyramid?
and the formula for the volume of a cone?

Answer 2

Yes, but I keep on getting the wrong answer. Can you walk me through it? @phi

Answer 3

what are the formula for the volume of a pyramid? and for a cone?

Answer 4

volume of pyramid is 1/3*b*h and volume of cone is 1/3*pi*r^2h

Answer 5

yes, and what is pi*r^2 ?

Answer 6

What do you mean?

Answer 7

pi*r^2 represents the *area of the base of the cone*

in other words, if we use "b" for area of the base, both formulas are the same

Answer 8

So would I set the two formulas equal to eachother and solve to find x^2?

Answer 9

They tell you
heights of the solids are equal (same h)
cross sectional areas...are equal (same "base area")

that means they will have the same volume (because they have the same base area and the same height h) and volume = ⅓ b h

Answer 10

which means, to find the volume of the cone, find the volume of the pyramid.

Answer 11

to find the volume of the pyramid, you need the area of its base.

its base is a triangle. to find the area of a triangle you need its base leg times its height divided by 2:
area= ½ b h (for a triangle)

can you find the legs of the right triangle?

Answer 12

I would use a^2+b^2+c^2 right?

Answer 13

I meant =c^2

Answer 14

you mean a^2+b^2=c^2

yes, you know "c" and one of the legs.

Answer 15

So once I get the other leg what formula do I use to get the area of the base

Answer 16

area= ½ b h (for a triangle)

for a right triangle, the base and height are just its legs.

Answer 17

After I get the area of the base I need to plug that info into the formula for the volume of a cone?

Answer 18

what did you get for the other leg of the triangle ?

Answer 19

I got 4.1. Is that right?

Answer 20

yes, but you might want to keep a few more decimals. say 4.123

now find the area of the triangle

Answer 21

Okay I got the 16.4. Is that correct?

Answer 22

not good enough. Use 4.123 for the length of your other side (not just 4.1)

Answer 23

16.492

Answer 24

What do I do with that?

Answer 25

that is b that you use in the formula
V= ⅓ b h

h is given as 17.

Answer 26

Thank you so much for the help! @phi