Question

if the volume of a right circular cone of height 9 cm is 48 pie cm cube find the diameter of the base​

Answer 1

Answer:

I am not fake but i am broken

Answer 2

$\mathtt{\huge{\underline{\bf{\green{Answer :- }}}}}$

8 cm

$\mathtt{\huge{\underline{\bf{\purple{Solution :- }}}}}$

Given :-

• The volume of a right circular cone is 48 π cm³.

• The hieght of a right circular cone is 9 cm.

To Find :-

• The diameter of the base.

Knowledge :-

A right circular cone is a cone in which the line joining vertex to mid point of its base must be perpendicular ( forms 90° angle).

Equation :-

(x²+y²+z²) cos²θ = (lx+my+nz)²

➝ (x²+y²+z²) = $\dfrac{(lx+my+nz)²}{cos²θ }$

Formulae related to cone :-

★ C.S.A /L.S.A. of cone = π r l

★ T.S.A of a cone = π(r + l) r

★ Volume of a cone = $\dfrac{1}{3 }$ π r² h

Solution :-

According to the question ,

The volume of a right circular cone is 48 π cm³.......(1)

Volume of a cone = $\dfrac{1}{3 }$ π r² h.......(2)

From 1 & 2 ,

$\dfrac{1}{3 }$ π r² h = 48 π cm³

Our hieght is 9 in the question .

➝ $\dfrac{1}{3 }$ × π × r² × 9 = 48 π cm³

➝ 3 π r² = 48 π cm³

➝ r² = $\dfrac{48 π}{3 π }$

➝ r² = $\cancel{\dfrac{48 π}{3 π }}$

➝ r² = 16

➝ r = √16

➝ r = 4 cm

The diameter of the base = 2 × r

➝ 2 × 4

➝ 8 cm.

The diameter of the base is 8 cm.

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