Tricky Geometry...?

Question

The volume of a sphere is equal to the volume of a right circular cylinder. The diameter of the sphere is equal to the altitude of the cylinder. What must be the base radius of the cylinder?
Pls. show ur solution.
Tnx very much!

Answer 1

let a be the radius of the sphere and b be the radius of the ©ylinder.

4πa³/3 = πb²h
and
2a = h

then ....
2a²/3 = b²

finally
b = a√(⅔)
there are infinitely many spheres and cylinders that can fit the situation. the above equation gives the radius of the cylinder in terms of the radius of the sphere.

Answer 2

Sphere of radius Rs and diameter Ds:-
Vs = (4/3) π Rs³
Vs = (4/3) π (Ds /2)³
Vs = (1/6) π Ds³
Cylinder of radius r and height h:-
Vc = π r² h

(π/6) Ds³ = π r² h
But Ds = h
h ³ / 6 = r² h
r² = h² / 6
r = √(1/6) (h)

Answer 3

Given: Shortest area of the triangle is 8 units. the different 2 components are x and (x + a million) units. --> The hypotheuse of the triangle is (x + a million) units. by way of Pythagoras' Theorem, 8^2 + x^2 = (x + a million)^2 sixty 4 + x^2 + x^2 + 2x + a million 2x = sixty 3 x = 31.5 subsequently, the climate of the triangle are 8 cm, 31.5 cm and 32.5 cm.

Answer 4

v1=v2
d=2r=h

(4/3)*pi*r^3=pi*r^2*h

dividing both sides by pi*r^2

(4/3)*r=h

(4/3)*r=h=2r

(4/3)r=2r

r=0

no possible solution i think