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(B) Given that the radius of the cylinder $(r_c)$ and the radius of the sphere $(r_s)$ are equal,so $r_c = r_s = 9 \, cm$.Let the height of the cylind

Vedclass · Accepted Answer

$12$

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(B) Given that the radius of the cylinder $(r_c)$ and the radius of the sphere $(r_s)$ are equal,so $r_c = r_s = 9 \, cm$.Let the height of the cylinder be $h$.The volume of the cylinder is given by $V_c = \pi r_c^2 h$.The volume of the sphere is given by $V_s = \frac{4}{3} \pi r_s^3$.According to the problem,the volumes are equal: $V_c = V_s$.Substituting the formulas: $\pi r_c^2 h = \frac{4}{3} \pi r_s^3$.Since $r_c = r_s = 9$,we can cancel $\pi$ and $r^2$ from both sides:$h = \frac{4}{3} r_s = \frac{4}{3} 	imes 9$.$h = 4 	imes 3 = 12 \, cm$.Thus,the height of the cylinder is $12 \, cm$.

Each of the radius of a cylinder and a sphere is $9 \, cm$. If the volumes of these solids are equal,find the height of a cylinder (in $cm$).

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