Question

A marble of radius 15 cm correctly fits under a cone.
The slant height of the cone is equal to the diameter
of its base. What is the height (in cm) of the cone?
(A) 253 (B) 45 (C) 30v2 (D) 60(3-1)​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

The height (in cm) of the cone is 45 cm.

Step-by-step explanation:

From question, a marble is inside the cone. So, the triangle is an isosceles triangle.

The radius, r is given by the formula:

$r=\frac{\text { Area }}{\text { Semiperimeter }}$

Where,

$Area=\frac{b h}{2}$

$Semiperimeter=\left[\frac{b+h+l}{2}\right]=\left[\frac{b+l+l}{2}\right]$

Now, the formula for radius becomes,

$r=\frac{\frac{b h}{2}}{\left[\frac{b+l+l}{2}\right]}$

Where,

b = base;

h = height;

I = slant height;

Now,

$15=\frac{b h}{b+2 l}$

From question, slant height of the cone is equal to the diameter  of its base.

b = l

Now,

$15=\frac{b h}{3 b}$

$15=\frac{h}{3}$

Thus, the height of the cone,

$\therefore h=45 \ \mathrm{cm}$