For this translate to a quadratic equation then solve using the quadratic formula. I need help with the steps

Question

A cylinder is to be made so that its volume is equal to that of a sphere with a radius of 9 inches. If a cylinder is to have a height of 4 inches, find its radius. I know the formulas for this but how do I implement them and the quadratic equation. Thanks!!!

Answer 1

a sphere with r=9" has a volume of
V=(4/3)π*9^3=972π
Volume of the cylinder is
V=972π=4π*r^2 divide both sides by 4π
243=r^2 take square root of both sides
r=9√3=15.588"

Answer 2

Vc = volume of cylinder
Vs = volume of sphere

Vc = pi*r^2*h
Vs = 4/3*pi*r^3

we know the two volumes equal. We also know r for the sphere (9 inches) and h for the cylinder (4 inches)

Vc = Vs
pi*r^2*4 = 4/3*pi*9^3
4r^2 = 36

putting into the quadratic form Ax^2 + Bx + C = 0
4r^2 + 0r - 36 =0

so A=4, B=0, and C = -36

r =(-b+/-sqrt(b^2-4ac))/(2a)
r = (+/- sqrt(-4*4*-36))/(2*4)
r = 3 and r = -3 but since r >=0 (no such thing as a negative radius)
r =3

Answer 3

a million) (x+4)^2 = (x)^2 + (x-2)^2 -15 isn't particularly actual. x, x-2 and x+4 are no longer consecutive weird and wonderful numbers, you would be able to desire to apply the two x, x+2 and x+4 or x-2, x and x+2 additionally, you would be able to desire to characteristic 15 to the appropriate factor of the equation (x+2)^2 = x^2 + (x-2)^2 + 15 or (x+4)^2 = x^2 + (x+2)^2 + 15 2) So, the equation for the fringe: x+y+a million.3 = 3.0 x+y = a million.7 and x^2 + y^2 = a million.3^2 = a million.sixty 9 so x^2 + y^2 +.01 = a million.7 and x^2 + y^2 + .01 = x + y 3) 20cm severe: h = 20cm and two times as long as that's extensive: l = 2w SA = 2lw+2lh+2wh SA = 4w^2 + 4wh + 2wh = 4w^2 +6wh = 1600 V = lwh = (2w)wh = 2hw^2 with a bit of luck which would be adequate to get you going.

Answer 4

V = (4π/3)9^3 = πr^2(4)
3r^2 = 9^3 = 729
Since you are required to have a quadratic equation,
r^2 - 243 = 0
Solving by quadratic formula,
(The coefficient of the r-term is 0)
r = (0 ±√(0 + 4*243))/2
r = ± (2√(243))/2
r cannot be negative, so
r = √243
r ≈ 15.58846

Answer 5

Volume of sphere = (4/3) pi r^3 = 972 pi. cu inches

Volume of cylinder is = pi x r x r x h = 4(r^2)pi

Now
4(r^2)pi = 972 pi
r^2 = 243
r = 15.6 inches

Answer 6

Volume of sphere = (4/3)pi.R^3
Volume of cylinder = pi.r^2.h

R=9
h=4
r=?

(4/3)pi.R^3 = pi.r^2.h
(4/3)R^3 = r^2h
r = sqrt ((4/3)R^3/h)
=sqrt(4/3 * 9^3 / 4)
=9sqrt(3)
=15.588 inches

Answer 7

Volume of sphere = (4/3)pi.R^3
Volume of cylinder = pi.r^2.h

R=9
h=4
r=?

(4/3)pi.R^3 = pi.r^2.h
(4/3)R^3 = r^2h
r = sqrt ((4/3)R^3/h)
=sqrt(4/3 * 9^3 / 4)
=9sqrt(3)
=15.588 inches (approx)