A cone of height and radius 10cm is cut along the midpoint of the height perpendicular to the height to get a conal region and a frustum. Find the volume of the conal region.
2006-12-19 02:19:04 · 10 answers · asked by Akilesh - Internet Undertaker 7 in Science & Mathematics ➔ Mathematics
The radius of the conal region = 1/2(10) = 5 cm
The height of the conal region = 1/2(10) = 5 cm
V=1/3Bh =1/3(25pi)(5) = (41 2/3)pi cm^3
approximately = 130.9 cm^3
2006-12-19 02:33:48 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
Since the diameter of the circle of the cone reduces from 10 cm at the bottom to 0 at the top, the diameter of the base of the conal region is 5 cm (since you have cut it half-way; You can prove this easily if you draw the cross section and compare the triangles). So the volume of the conal region
= 1/3 pi *(r) sq * h = 1/3*22/7*25*5 = 130.95 cc
2006-12-19 02:39:10 · answer #2 · answered by saudipta c 5 · 0⤊ 0⤋
The cone is cut along the midpoint of the height, perpendicular to the height.
This means you slice the top of the cone off at h/2 (or 5cm since this problem states that the height is 10cm).
You are also told that the radius of the original cone's height is equal to the height of the original cone. Since the "new" cone made by cutting off the top of the old cone has the same shape as the old cone it can be thought of as a scale model. That means that the radius of the "new" cone is equal to the height of the "new' cone (or 5cm).
Now you have height and radius of the cone. You can plug these numbers into the equation to find the volume of the cone.
V = 1/3 Area of Base * height
or
V=1/3*pi*(r^2)*h
use the height and radius of the "new" cone and plug them in.
HINT: Drawing a picture of your geometry problems will often help you understand the question better.
2006-12-19 02:33:39 · answer #3 · answered by Annie 3 · 1⤊ 0⤋
as the cone is cut mid way ........thus the 2 triangles are similar i.e. the big cone triangle and the smaller one.............. thus their ratio of sides is also equal ..............as the perpendicular is halved thus the radius is also halved.............thus radius and height of smaller cone also become half i.e 5 each . thus
Volume:1/3 (pi) r*r *h = 1/3*(3.14)*5*5*5=130.833
2006-12-19 02:41:35 · answer #4 · answered by nasty_malhi 1 · 0⤊ 0⤋
volume of a cone=1/3*3.14*r*r*h
=1/3*3.14*10*10*5
=523.333
2006-12-19 02:29:39 · answer #5 · answered by Anonymous · 0⤊ 0⤋
jointly as I kinda like math, and that i've got doodled my way by using numerous instructions, of the two the highschool and school point, I in no way concept to combine the two, or observed a connection. great link Des, thank you! i'm going to ought to bypass it directly to my son who's a math wizard whilst in comparison with myself. I do love soduko, and good judgment issues, yet have not gotten my son further engaged. whilst he substitute into youthful, we did do fairly some counting and sorting in our on a regular basis existence for the exciting of it, and along with his Asperger's he regarded interested in the sorting, no longer that I constantly understood how issues have been taken care of, lol.
2016-10-18 11:52:08 · answer #6 · answered by ? 4 · 0⤊ 0⤋
the new cone must be having volume half that of the original cone. so calculate the volume of the original cone and divide it by 2.
2006-12-19 02:33:20 · answer #7 · answered by sri_july27 2 · 0⤊ 1⤋
i hate this ...i had to do that kind of stuff like 2 weeks ago....i never got the hang of it! sorry!
2006-12-19 02:22:23 · answer #8 · answered by Anonymous · 0⤊ 0⤋
answer is "520 cm cube"
2006-12-19 03:09:49 · answer #9 · answered by cham 2 · 0⤊ 0⤋
523.809523cm
2006-12-19 02:33:31 · answer #10 · answered by Ricky2cool 2 · 0⤊ 0⤋