Question

the height and the slant height of a cone are 21 cm and 28 cm respectively. find the volume of the cone​

Answer 1

Answer:

7546 cm3

Explanation:

Given that:

Slant height of the cone = l =28 cm

Height of the cone = h = 28 cm

Let the radius of the cone = r cm

As we know that triangle AOB in the cone is right angled so let us use Pythagoras theorem in order to find the radius of the cone:

In right angled ΔAOB

AO=21cm,OB=(r)cm&BA=28cm

Let us use Pythagoras theorem for right angled triangle AOB.

According to Pythagoras theorem, for right angled triangle:

(Hypotenuse)2=(Side1)2+(Side2)2

Using the same for the given triangle AOB we get:

⇒(AB)2=(AO)2+(OB)2

Substituting the value in the equation we get:

⇒(l)2=(h)2+(r)2⇒(28)2=(21)2+(r)2⇒(r)2=(28)2−(21)2⇒(r)2=(28+21)(28−21) [∵(x)2−(y)2=(x+y)(x−y)]⇒(r)2=(49)(7)⇒r=49×7−−−−−√⇒r=77–√cm

Now as we have the radius of the cone, we can easily find the volume of the cone.

As we know that volume of the cone is 13πr2h

So let us find the volume of the cone.

Volume:

=13πr2h=(13π(77–√)221)cm3

Now, let us simplify the term:

=(13×227×77–√×77–√×21)cm3=(13×227×7×7×7×21)cm3=(22×7×7×7)cm3=7546cm3

Hence, the volume of the cone is 7546cm3 .