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

Answer:

The Vertical height of the frustum is 6 cm.

Among the given options option (a) 6 cm is the correct answer.

Step-by-step explanation:

Given :  

Radius of circular end of a  frustum ,R = 14 cm

Radius of circular end of a  frustum ,r = 6 cm

Slant Height of the frustum (l) = 10 cm

Let the vertical height of the frustum be h  

Slant height of a frustum , l = √(R - r)² + h²

l² = (R - r)² + h²

[On squaring both sides]

10² = (14 - 6)² + h²

100 = 8² + h²

100 = 64 + h²

h² = 100 - 64

h² = 36

h = √36

h = 6 cm

Vertical height of the frustum  = 6 cm

Hence, the Vertical height of the frustum is 6 cm.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

GIVEN :

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

Longer radius { R } = 14cm

Shorter radius { r } = 6cm

Slant Height of the frustrum = 10cm

Vertical height be x

We know that,

l² = h² + { R - r }²

(10)² = h² + { 14 - 6 }²

100 = h² + { 8 }²

100 = h² + 64

h² = 100 - 64

h² = 36

h = √36

h = 6cm

Therefore, the vertical height is 6cm.