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
(a)6 cm
(b)8 cm
(c)4 cm
(d)7 cm

Answer 1

Given,

The radii of circular ends of a frustrum are 6cm and 14cm

Slant height of the frustrum = I = 10cm

Let R be the radius of bigger circle = 14cm

r be the radius of small circle = 6cm

Let the verticle be "h"

I^2= h^2 { R - r } ^2

10^2 = h^2 { 14 - 6 }^2

100 = h^2 {8}^2

100 = h^2 {64}

h^2 = 100 - 64

h = √36

h = 6

Therefore, the vertical height of the frustrum is 6cm.

Answer 2

Answer : Opt. ( a ) 6 cm

Step by step explanation :

Given :

Radius of the circular ends of frustum = 6 cm and 14 cm respectively.

Let r1 be 6 cm and r2 be 14 cm.

Slant height ( L ) = 10 cm

Vertical height ( h ) = ?

We know that,

$\tt{L = \sqrt{ {h}^{2} + (r1 - r2) {}^{2} }}$

Now,

Squaring both the sides,

$\tt{L {}^{2} = h {}^{2} + (r1 - r2) {}^{2} }$

$\tt{\therefore h {}^{2} = L {}^{2} - (r1 - r2) {}^{2}}$

$\tt{h {}^{2} = (10) {}^{2} - (14 - 6) {}^{2}}$

$\tt{h {}^{2} = 100 - (8) {}}^{2}$

$\tt{h {}^{2} = 100 - 64}$

$\tt {h {}^{2} = 36}$

Square rooting both sides,

$\tt{h = 6}$

Thus,

Vertical Height = 6 cm

Hence, Opt. ( a ) is the answer.