and the radius of the sphere is 8m, then
h cubed minus 24h squared plus 205=0
Then find h, the height of the dome, given that its value is between 1m and 6m.
I got the answer to be around 3.14m high, but can anyone be more accurate. Thanks.
2007-01-17 07:25:24 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Using πh²(r-1/3h) to improve your answer:
πh²(r-1/3h) = 215 m²
πh²r-1/3πh^3 = 215 m²
h²r-1/3h^3 = 215/π m²
8h²-1/3h^3 = 215/π m²
h² - 1/24h^3 = 215/ 8π m²
24h² - h^3 = 24 * 215/ 8π m²
24h² - h^3 = 3 * 215/ π m²
24h² - h^3 = 645 / π m²
h^3 - 24h² = -645 / π m²
h^3 - 24h² + 645π = 0 m²
h^3 - 24h² + 205∙309 8766 = 0 m²
Using this formula may help to improve your accuracy.
2007-01-17 13:34:27 · answer #1 · answered by Brenmore 5 · 0⤊ 0⤋
h^3 - 24h^2 + 205 = 0
Solving numerically, there is only one root 0 < x < 8:
x â 3.134455194
check:
3.134455194^3 - 24*3.134455194^2 + 205 =
30.795 - 235.795 + 205 = 0
2007-01-17 08:13:36 · answer #2 · answered by Helmut 7 · 0⤊ 0⤋
The root lies between 3.14454 and 3.134469
Use Newton's method to get any degree of accuracy you want.
2007-01-17 08:17:48 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
Do your own home work, it will make you smarter.
2007-01-17 07:32:51 · answer #4 · answered by Anonymous · 0⤊ 1⤋