Question

4. )If the volume of a right circular cone of height 9 cm is 48 πcm^3, find the diameter of its
base.​

Answer 1

Given :-

Volume of the cone = 48πcm³

Height of the cone = 9 cm

Required to find :-

• The diameter of the base ?

Formula used :-

$\tt{ volume \: of \: the \: cylinder = \dfrac{1}{3} \pi r^2 h }$

Solution :-

Given information ;

Volume of the cone = 48πcm³

Height of the cone = 9 cm

we need to find the diameter of the base .

So,

Let's consider the radius of the cone = x

Since ,

we know that ;

Volume of a cone = 1/3 π r² h

By substituting the values we get ;

48π = 1/3 π x x² x 9

48 x π = 1/3 π x x² x 9

π ( pi ) get's cancelled on both sides ;

48 = 1/3 x² x 9

48 x 3 = 9x²

9x² = 48 x 3

x² = 48 x 3/9

x² = 48/3

x² = 16

x = √16

x = +4 or - 4

Since, length can't be in negative

x = 4 cm

Hence,

value of x is 4 cm

So,

Radius of the cone = 4 cm

However ;

We know that ;

Diameter = Radius x 2

So,

Diameter = 4 x 2

Diameter = 8 cm

Therefore ,

Diameter of the base = 8 cm

Diagram ;

$\setlength{\unitlength}{40} \begin{picture}(6,6) \qbezier(2,2)(3.5,1)(5,2) \qbezier(2,2)(3.5,3)(5,2)\qbezier(2,2,)(2.8,3.5)(3.5,5)\qbezier(5,2,)(4.2,3.5)(3.5,5)\put(2,2){\line(1,0){3}}\put(3.5,2){\line(0,1){3}}\put(3.5,3){\vector(1,1){1.25}}\put(3.8,2){\vector(1,1){1.25}}\put(5,3){ \tt Diameter }\put(4.8,4){ \tt Height = 9 \: cm }\put(6,0){\boxed{ \bf @MisterIncredible }}\end{picture}$

Answer 2

Given ,

• Height of cone (h) = 9 cm
• Volume of cone = 48π cm³

We know that , the volume of cone is given by

$\large \boxed{ \sf{Volume = \frac{\pi {r}^{2}h }{3} }}$

Thus ,

$\sf \mapsto 48\pi = \frac{\pi \times {(r)}^{2} \times 9 }{3} \\ \\ \sf \mapsto {(r)}^{2} = 16 \\ \\ \sf \mapsto r = ±4 \: cm$

Since , the length can't be negative

Therefore , the radius of cone is 4 cm

We know that ,

Diameter = 2 × Radius

Thus ,

Diameter of cone = 2 × 4

Diameter of cone = 8 cm

$\sf \therefore{\underline{The \: diameter \: of \: cone \: is \: 8 \: cm}}$