Question

4. If the volume of a right circular cone of height 9 cm is 48 π cm, find the diameter of its base.
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Answer 1

★ Correct Question:

If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.

★ Solution:

Height of the right circular cone = 9 cm

Radius of the cone = r cm

Formula to find volume of a cone = $\sf{\dfrac{1}{3}\pi\:r^2h}$ ----- (1)

Given volume = 48π cm³ ----- (2)

Combining statements (1) and (2):

= 1/3πr²h = 48π cm³

→ Substituting the values in the equation:

$\sf{=\dfrac{1}{3}\pi\:r^2\times9=48\pi\:cm^3}$

→ Cancelling the like terms:

$\sf{=\pi\:r^2\times3=48\pi\:cm^3}$

→ Moving the constant terms to the RHS:

$\sf{r^2=\dfrac{48\pi}{3\pi}}$

→ Cancelling the like terms:

$\sf{r^2=16}$

r² = 16.

So,

r = √16

r = 4 cm

Here, we are asked to find the diameter:

Diameter = 2 x radius

= 2 x 4

= 8 cm

Hence the diameter of the cone is 8 cm.

Knowledge Bytes:

→ Important Volume Formulae:

✳ Volume of cuboid = lbh

✳ Volume of cube = a³

✳ Volume of cylinder = πr²h

✳ Volume of cone = 1/3πr²h

✳ Volume of sphere = 4 /3πr³

Answer 2

Step-by-step explanation:

volume of cone= π(r^2)h/3

48π=π(r^2)9/3

48=3(r^2)

16=r^2

r=4

diameter=2r

=2x4

=8cm