If the volumes of a cone and a hemisphere having the same base are equal, then the height of the cone will be $x$ times the radius of the base of hemisphere, where $x$ is

Question

If the volumes of a cone and a hemisphere having the same base are equal- then the height of the cone will be x times the radius of the base of hemisphere- where x is123pi

Toppr Admin · Accepted Answer

If r is the radius of the sphere and h be the height of the cone- thenvolume of the hemisphere -23-x3C0-r3-and volume of the cone -13-x3C0-r2h-Given- 23-x3C0-r3-13-x3C0-r2h-x2234- h-2r-x2234-hr-2i-e- x-2

If the volumes of a cone and a hemisphere having the same base are equal, then the height of the cone will be $x$ times the radius of the base of hemisphere, where $x$ is
$1$
$2$
$3$
$π$

If $r$ is the radius of the sphere and $h$ be the height of the cone, then
volume of the hemisphere $= \frac{2}{3} π r^{3}$ ,
and volume of the cone $= \frac{1}{3} π r^{2} h$ ,
Given, $\frac{2}{3} π r^{3} = \frac{1}{3} π r^{2} h$
$∴$ $h = 2 r$
$∴ \frac{h}{r} = 2$
i.e. $x = 2$

If the volumes of a cone and a hemisphere having the same base are equal, then the height of the cone will be x times the radius of the base of hemisphere, where x is123π

If r is the radius of the sphere and h be the height of the cone, thenvolume of the hemisphere =23πr3,and volume of the cone =13πr2h,Given, 23πr3=13πr2h∴ h=2r∴hr=2i.e. x=2

If the volumes of a cone and a hemisphere having the same base are equal, then the height of the cone will be $x$ times the radius of the base of hemisphere, where $x$ is
$1$
$2$
$3$
$π$

If $r$ is the radius of the sphere and $h$ be the height of the cone, then
volume of the hemisphere $= \frac{2}{3} π r^{3}$ ,
and volume of the cone $= \frac{1}{3} π r^{2} h$ ,
Given, $\frac{2}{3} π r^{3} = \frac{1}{3} π r^{2} h$
$∴$ $h = 2 r$
$∴ \frac{h}{r} = 2$
i.e. $x = 2$