Question

The volume of a hollow hemispherical vessel with internal radius 3 cm is 126π cm cube. The external diameter of the hemispherical vessel is

Answer 1

Answer:

Volume of hemisphere = 2/3*π*r³

Volume of hemispherical shell will be 2/3*π*(R³-r³).

where R is outer radius and r is inner radius.

putting r=3 and equating above equation with 126π, we get

2/3*π*(R³-27) = 126*π

Solving this equation, we will get

R³-27  = 189

R³ = 216

R = 6.

Since R is equal to 6, diameter will be twice of it, i.e 12

Answer 2

Answer:

6 cm

Step-by-step explanation:

Let the inner radius of the hollow vessel be r = 3 cm and outer radius be R = ?.

According to the question,

volume of the material used in making the vessel = volume of hemi. with radius R - volume of hemi. with radius r.

$\implies 126 \pi = \dfrac{2}{3} \pi R^3 - \dfrac{2}{3} \pi r^3\\\\\\\implies 126 \pi = \dfrac{2}{3} \pi (R^3 - 3^3)\\\\\\\umplies 126 = \dfrac{2}{3} (R^3 - 27)\\\\\\\implies 126 \times \dfrac{3}{2} = R^3 - 27\\\\\\\implies 189 + 27 = = R^3\\\\\\\implies 216 = R^3\\\\\\\implies R = \sqrt[3]{216} = \bold{6 \; \; cm}$