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Mathematics

If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is :

  1. 13\dfrac{1}{3} πr3

  2. 23\dfrac{2}{3} πr3

  3. 3 πr3

  4. 9 πr3

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Answer

Given, radius = 3r and height(h) = 3r

Volume of cone = 13\dfrac{1}{3} πr2h

=13×π×(3r)2×3r=π×9r2×r=9πr3= \dfrac{1}{3} \times π \times (3\text{r})^2 \times 3\text{r} \\[1em] = π \times 9\text{r}^2 \times \text{r} \\[1em] = 9 π\text{r}^3

Hence, option 4 is the correct option.

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