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

Answer 1

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"`