A square pyramid resting on its base is filled to half its height with 320 cubic centimeters of water. How much water is needed to finish filling the rest of the pyramid?
2007-04-29 14:06:44 · 3 answers · asked by Sally C 1 in Science & Mathematics ➔ Mathematics
The bottom half comprises 7/8 of the volume. (How did I get that? Double each dimension of any solid object, and the volume has to increase 2³ = 8 times.) So, you need 320/7 = 45.7cm³ more.
2007-04-29 14:10:20 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The bottom half of the pyramid (as measured by height) comprises 7/8ths of the volume of the pyramid. So 1/8th of the volume remains to be filled.
Let
V = Volume of pyramid
(7/8)V = 320
The remaining amount needed to fill the pyramid is:
(1 - 7/8)V = (1/8)V = 320/7 = 45 5/7 cc
2007-04-29 14:16:23 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
volume of pyramid = 1/3 height * base^2
320 cucm = 1/3 height * base^2 - 1/3 height/2 * (base/2)^2
320 = 1/3 h * b^2 - 1/3 h/2 * b^2/4
320 = 1/3 (hb^2 - hb^2/8)
320 = 1/3 (7hb^2/8)
320/7 = 1/3 hb^2/8
45.714 cucm
2007-04-29 14:19:41 · answer #3 · answered by rooster1981 4 · 0⤊ 0⤋