Question

the volume of a hollow hemispherical vessel with internal radius 3cm is 126piecm.the external daimeter of hemispherical vessel is​

Answer 1

Answer:

12 cm

Step-by-step explanation:

1.) The volume of a hollow hemispherical vessel is given by the formula

$V=\frac{2\pi}{3} (R^3- r^3 )$

where R is the outer radius and r is the inner radius

2.) Solving for the outer radius R, we have

$R=\sqrt[3]{r^3+\frac{3V}{2\pi}}$

3.) Substituting r=3 and V=126π, we get

$R=\sqrt[3]{27+189}=\sqrt{216}=6$

4.) The outer diameter is $2R=12cm$

Answer 2

Answer:

12 cm

option 3

Step-by-step explanation:

Hollow hemi sphere

so volume of hemisphere here is the actually volume of material used.

Let say external radius = R

then Volume = (2/3)πR³

Volume with internal radius = (2/3)π3³

so volume of materiel = (2/3)πR³ - (2/3)π3³

(2/3)πR³ - (2/3)π3³  = 126π

=> R³ - 27 = 189

=> R³ = 216

=>R = 6

Diameter = 2R = 12 cm

Option 3 is correct