Solve the following mathematical problems:

A hemisphere and a right circular cone on equal bases are of equal height. Find the ratio of their volumes.

Created: 2 months ago | Updated: 2 months ago

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Here, r = Radius; h = Height
We know, the volume of a sphere = $\frac{4}{3} {πr}^{3}$
The volume of hemisphere= $\frac{4}{2 \times 3} {πr}^{3} = \frac{2}{3} {πr}^{3}$
We also know, the volume of cone = $\frac{1}{3} {πr}^{2} h$

Given, that hemisphere and cone have equal bases and the same height
Volume of hemisphere: volume of cone 3

$= \frac{2}{3} {πr}^{3} : \frac{1}{3} {πr}^{2} h = \frac{2}{3} {πr}^{3} : \frac{1}{3} {πr}^{2} \times h = \frac{2}{3} {πr}^{3} : \frac{1}{3} {πr}^{3} [As both the height is same] = \frac{2}{3} : \frac{1}{3}$ [dividing both by ${πr}^{3}$

=2 : 1 [Multiplying both by 3]
Ratio of hemisphere and cone = 2 : 1

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simplify: $\frac{5 x + 2}{x^{2} - x - 20} + \frac{2 x - 1}{x^{2} - 4 x - 5}$

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Solve the following mathematical problems:

Find the H.C.F. of $x^{3} - 16 x, 2 x^{2} + 9 x^{2} + 4 x, 2 x^{3} + x^{3} - 28 x$

Created: 2 months ago | Updated: 2 months ago

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Solve the following mathematical problems:

A hemisphere and a right circular cone on equal bases are of equal height. Find the ratio of their volumes.

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