Question

3.If the volume of a right circular cone of height 9 cm is 48 cm 3 , find the diameter(approx.) of
its base.

Answer 1

Given :-

• Volume of right circular cone = 48 cm³
• Height = 9 cm

To find :-

• Diameter of cone

Solution :-

As we know that,

☛ Volume of cone = ⅓ × (πr²h)

Putting values :

⇒ 48 = ⅓ (22/7 × r² × 9)

⇒ 48 × 3 = 22/7 × 9r²

⇒ 144 = 22/7 × 9r²

⇒ 144 = 198r²/7

⇒ 144 × 7 = 198r²

⇒ 198r² = 1008

⇒ r² = 1008/198

⇒ r² = 5.091

⇒ r = √5.091

⇒ r = 2.256 cm [Approx.]

So, radius of its base = 2.256 cm (Approx.)

Now we know that,

☛ Diameter = 2 × Radius

⇒ Diameter = 2 × 2.256

⇒ Diameter = 4.512 cm [Approx.]

Therefore,

Diameter of its base = 4.512 cm (Approx.)

Answer 2

GIVEN:

Volume of a right circular cone = 48cm³

Height of the cone = 9cm

TO FIND:

Diameter of the base of cone.

SOLUTION:

We know that,

Volume of cone = 1/3 π r² h

1/3 × 22/7 × r² × 9 = 48cm³

22/7 × r² × 3 = 48cm³

22/7 × r² = 48/3

==> r² = 16 × 7/22

==> r² = 112/22

==> r √5.09

==> r = 2.25

Radius of the base of cone = 2.25cm

Diameter of the cone = 2.25 × 2 = 4.5cm

Therefore, the diameter of the cone is 4.5cm.