Question

a sphere and a right circular cylinder of the same radius have equal volume by what percent does the diameter of cylinder is exceeds its height

Answer 1

Volume of circle=4/3(22/7r^3)

Volume of cylender=22/7r^2h

As volumes are same:-

4/3(22/7r^3)=22/7r^2h

4/3r=h

As diameter is twice the radius

r=1/2d

4/3×1/2d=h

2/3d=h

h=66.667%(Approx)

(2/3×100=66.667)

Answer 2

Answer:

50%

Solution:-

Let the given sphere and cylinder have same radius r and also let the height of the cylinder be h

Then,

Volume of sphere=volume of cylinder

$\frac{4}{3}\pi {r}^{3} = \pi {r}^{2}h$

$r = \frac{3h}{4}$

$2r = \frac{3h}{2}$

$d = \frac{3h}{2}$

Thus the diameter of the cylinder=3h/2

Excess of diameter of cylinder

$\frac{3h}{2} - h$

$\frac{h}{2}$

$excess\% = ( \frac{h}{2} \times \frac{1}{h} \times 100)\%$

$50\%$