Question

the slant height of the frustum of a cone is 5cm.if the difference between radii of its 2 circular ends is 4cm find the height of the frustum

Answer 1

QUESTION :-

the slant height of the frustum of a cone is 5cm.if the difference between radii of its 2 circular ends is 4cm find the height of the frustum?

ANSWER:-

Let r and R be the radius of the circular ends of the frustum of the cone and h be the height of the frustum.

R-r = 4 and l = 5 cm

l²= (R-h)² + h² ---- [formula]

5² = 4² + h²

h² = 25 - 16

h² = 9

h=√9

h=3cm.

Hence , height of the frustum is 3 cm.

✨✨THANKS ✨✨

Answer 2

Answer:

The height of the frustum is 3 cm.

Step-by-step explanation:

Given :

The slant height (l) of the frustum of a cone = 5 cm.

Consider the :

Radius of the larger circular face of the frustum as - R cm.

The Radius of the smaller circular  face of the frustum as - r cm.

According to the question,

⇒ R - r = 4cm.

As we know :

$\bigstar\;\boxed{\bf L=\sqrt {h^{2}+(R-r)^{2}}}$

So,

$\sf \implies 5=\sqrt{ h^{2}+4^{2}}$

Now, Squaring both sides of the equation,

$\sf\\\implies 5^{2}= h^{2}+4^{2}\\ \\ \sf \implies 25-16= h^{2}\\ \\ \sf \implies 9 = h^{2}\\ \\ \sf \implies \sqrt{9} = h \\ \\ \sf \implies h = 3\: cm$

∴ Height of the frustum (h) = 3cm.