Question

A sphere and a right circular cylinder of the same radius have equal volumes.By what percentage does the diameter of the cylinder exceed its height

Answer 1

A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the circle exceed its height?

Volume of a cylinder=πr2h

Volume of a sphere=43πr3

Equating both, we get

43r=h

2r=3h2

Diameter, d=2r=3h2

Now, d−h=h2

d−hh=12

Hence, the percentage by which the diameter exceeds the height=(d−h)h×100=50%

Answer 2

Answer:

50℅

Solution:-

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

Then,

Volume of sphere=Volume of cylinder

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

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

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

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

Thus the diameter of the cylinder is 3h/2

Excess of diameter of cylinder over it's height

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

$\frac{h}{2}$

Excess℅

$\frac{h}{2} \times \frac{1}{h} \times 100\%$

$50\%$

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Excess=50℅