The radius and height of a right circular con | vedclass

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(C) Let the radius $r = 3x$ and the height $h = 4x$.The volume of a right circular cone is given by $V = \frac{1}{3}\pi r^2 h$.Substituting the given

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$10$

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(C) Let the radius $r = 3x$ and the height $h = 4x$.The volume of a right circular cone is given by $V = \frac{1}{3}\pi r^2 h$.Substituting the given values: $96\pi = \frac{1}{3}\pi (3x)^2 (4x)$.Simplifying the equation: $96\pi = \frac{1}{3}\pi (9x^2)(4x) = 12\pi x^3$.Dividing both sides by $12\pi$: $x^3 = \frac{96}{12} = 8$.Taking the cube root: $x = 2$.Thus,the radius $r = 3(2) = 6\, cm$ and the height $h = 4(2) = 8\, cm$.The slant height $l$ is given by $l = \sqrt{r^2 + h^2}$.$l = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10\, cm$.

The radius and height of a right circular cone are in the ratio $3: 4$. If its volume is $96\pi\, cm^3$,what is its slant height (in $cm$)?

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