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Question
The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is
Options
6 cm
8 cm
4 cm
7 cm
Solution
Radii of circular ends of frustum
`r_1 = 14 "cm" , r_2 = 6"cm "`
Slant height
`l = 10"cm , h" = ?`
`l = sqrt (h^2 + (r_1 - r_2)^2)`
`l^2 = h^2 + (r_1 - r_2)^2`
{squaring on both sides}
`h^2 = l^2 - (r_1 - r_2)^2`
`h^2 = (10)^2 - (14 - 6)^2`
`h^2 = 100 - 64`
`h^2 = 36`
`h = 6 "cm"`
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