A cone has a volume of 10mcubed.
The vertical height of the cone is 1.5m.
Calculate the radius of the base of the cone correct to 3 significant figures
2007-02-22 07:06:16 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Volume = Area of base times height/3
V = ah/3
10 = a (1.5/3)
a = 20 sq m
area of base = pi(r^2) =20
r^2 =20/pi= 20/3.1416 = 6.366
r = 2.523 m
2007-02-22 08:52:11 · answer #1 · answered by bignose68 4 · 0⤊ 0⤋
think of slicing the cone interior the vertical course, by a diagonal of the cube. Then decrease it returned interior the vertical course, contained in direction of the leftover vertex. you have 1 / 4 of a cone and 1 / 4 of a cube. you will see 2 comparable triangles. the vast suitable triangle would have base r = 8, top h = 5, and its hypotenuse would be an part on the exterior of the cone. The smaller suitable triangle would have an fringe of top x, a base 8 - 0.5 x sqrt(2), and a hypotenuse which would be an part on the exterior of the cone. right here x = length of the cube. How did i'm getting the backside? The diagonal of the cube = x sqrt(2) by using fact that's the hypotenuse of a 40 5-40 5 triangle. using comparable triangles, (5/8) = x / ( 8 - 0.5 x sqrt(2) ) 5 - x (5/sixteen) sqrt(2) = x x (a million + (5/sixteen) sqrt(2) ) = 5 x (sixteen + 5 sqrt(2) ) = 5 (sixteen) x = eighty / (sixteen + 5 sqrt (2) ) answer: x = 4.6 inches
2017-01-03 08:46:47 · answer #2 · answered by Anonymous · 0⤊ 0⤋
A = 1/3 πr²*h
2007-02-22 07:09:51 · answer #3 · answered by E 5 · 0⤊ 0⤋
37.346
2007-02-22 07:09:09 · answer #4 · answered by god knows and sees else Yahoo 6 · 0⤊ 0⤋