Question

In the figure, a right pyramid with a square base is divided into three parts A,B and C by two planes parallel to the base such that the lengths of their slant edges are 1cm, 2cm and 3 cm respectively.
Find the volume of A : volume of B : volume of C.

Answer 1

i hate drawing very much

Answer 2

@Callisto @hartnn

Answer 3

Consider 3 figures:
A, A and B, A and B and C

Since the three figures are similar figures, (ratio of sides)^3 = (ratio of volumes)
So far so good?

Answer 4

yup

Answer 5

(1:2:3)^3 = (?,?,?)
^ Fill in the blanks

Answer 6

B=(7-3-1)^3=27??
C=(7-2-1)^3=64???

Answer 7

1:8:27

Answer 8

but the answer is not 1:8:27 o.0

Answer 9

Volume of A : A and B : A and B and C = 1:8:27. Right.
Now, we need to find Volume of A : B : C. Have any idea how to get it?

Answer 10

nope ._.

Answer 11

1:(8-1):(27-8-1)?

Answer 12

YES YES YES

Answer 13

1:7:18?

Answer 14

the answer is 1:26:189 lol

Answer 15

OMG!!! My careless mistakes!!
ratio of sides A : A and B : A and B and C = 1: (1+2) : (1+2+3) = ...?

Answer 16

1:3:6

Answer 17

(1:3:6)^3 = ?

Answer 18

1:27:216

Answer 19

Use the same trick

Answer 20

to get the volume ratio you need

Answer 21

1:27-1:216-27
=1:26:189 :P

Answer 22

Yes. I am sooooo careless :\