If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r- then the height of the cone-

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Toppr Admin · Accepted Answer

Radius of sphere-2r-Radius of cone-r-Volume of sphere-dfrac-4-3-pi-2-3-dfrac-32-3-pi r-3-Volume of cone-dfrac-1-3-times -pi r-2h-dfrac-pi r-2h-3-Given volume of sphere and cone are equal-therefore -dfrac-32-pi r-3-3-dfrac-pi r-2h-3-h-32r-

If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.

Radius of sphere$$=2r$$
Radius of cone$$=r$$
Volume of sphere$$=\dfrac{4}{3}\pi(2)^3=\dfrac{32}{3}\pi r^3$$
Volume of cone$$=\dfrac{1}{3}\times \pi r^2h\dfrac{\pi r^2h}{3}$$
Given volume of sphere and cone are equal.
$$\therefore \dfrac{32\pi r^3}{3}=\dfrac{\pi r^2h}{3}$$
$$h=32r$$.

If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.

Radius of sphere$$=2r$$Radius of cone$$=r$$Volume of sphere$$=\dfrac{4}{3}\pi(2)^3=\dfrac{32}{3}\pi r^3$$Volume of cone$$=\dfrac{1}{3}\times \pi r^2h\dfrac{\pi r^2h}{3}$$Given volume of sphere and cone are equal.$$\therefore \dfrac{32\pi r^3}{3}=\dfrac{\pi r^2h}{3}$$$$h=32r$$.

Radius of sphere$$=2r$$
Radius of cone$$=r$$
Volume of sphere$$=\dfrac{4}{3}\pi(2)^3=\dfrac{32}{3}\pi r^3$$
Volume of cone$$=\dfrac{1}{3}\times \pi r^2h\dfrac{\pi r^2h}{3}$$
Given volume of sphere and cone are equal.
$$\therefore \dfrac{32\pi r^3}{3}=\dfrac{\pi r^2h}{3}$$
$$h=32r$$.