Find the slant height of a frustum cone whose top radius is 12 m and bottom radius is 10 m. The height of the cone is 13 m.

13.15 m

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12.15 m

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10.15 m

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14.25 m

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Solution

The correct option is D 13.15 m
For a frustum of cone, if $h$ is the height, $r_{1}$ is the base radius, $r_{2}$ is the top radius, slant height is $l$
Then slant height, $l^{2} = h^{2} + (r_{1} - r_{2})^{2}$
$\Rightarrow l^{2} = 13^{2} + (12 - 10)^{2}$
$\Rightarrow l^{2} = 169 + 4$
$\Rightarrow l^{2} = 173$
$\Rightarrow l = 13.15 m$

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Find the slant height of a frustum cone whose top radius is 12 m and bottom radius is 10 m. The height of the cone is 13 m.

The correct option is D 13.15 mFor a frustum of cone, if h is the height, r1 is the base radius, r2 is the top radius, slant height is lThen slant height, l2=h2+(r1−r2)2⇒l2=132+(12−10)2⇒l2=169+4⇒l2=173⇒l=13.15m