The slant height and height of a frustum of a cone are 5 cm and 4 cm respectively. If the circumference of one of its ends is 44 cm, then the radius of the other end can be

3 cm

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5 cm

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8 cm

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10 cm

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Solution

The correct option is D 10 cm
Slant height (l) = 5 cm

Height (h) = 4 cm

Let radii of its ends be $r_{1} a n d r_{2}$

Now, the circumference of one end is 44 cm

$\Rightarrow 2 \times \frac{22}{7} \times r_{1} = 44$

$\Rightarrow r_{1} = 7 c m$

Since, $l^{2} = h^{2} + (r_{1} - r_{2})^{2}$

$\Rightarrow 25 = 16 + (7 - r_{2})^{2}$

$\Rightarrow 9 = 49 + r_{2}^{2} - 14 r_{2}$

$\Rightarrow r_{2}^{2} - 14 r_{2} + 40 = 0$

$\Rightarrow r_{2}^{2} - 10 r_{2} - 4 r_{2} + 40 = 0$

$\Rightarrow r_{2} (r_{2} - 10) - 4 (r_{2} - 10) = 0$

$\Rightarrow (r_{2} - 4) (r_{2} - 10) = 0$

$\Rightarrow r_{2} = 10 c m o r 4 c m$

Hence, the correct answer is option (d).

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