Maths question from Naib Tehsildar exam, 2018 by JKSSB
If the diameter of the internal and external surface of a hollow hemispherical shell are 12 cm and 8 cm respectively, then the volume of the solid part in the hemisphere shell is
Last updated Jun 24, 2026
Correct Answer:
Option B —
304π/3 cm³
To find the volume of the solid part of a hollow hemispherical shell, we subtract the volume of the internal empty space from the total volume of the external hemisphere.
1. The Formula
The volume (V) of a solid hemisphere is given by: V = 2\3pi R^3
For a hollow shell with external radius (R) and internal radius (r), the volume of the solid part is:{Volume} = 2\3}pi(R^3 - r^3)
2. Step-by-Step Calculation
Step 1: Identify the radii The problem provides diameters, so we must first divide them by 2:
External Radius (R): 12cm\2 = 6cm
Internal Radius (r) : 8cm \2 = 4 cm
(Note: In the question wording, 12 cm refers to the larger external surface and 8 cm to the smaller internal surface).
Step 2: Calculate the cubes of the radii
R^3 = 6^3 = 216 cm^3
r^3 = 4^3 = 64cm^3
Step 3: Plug the values into the formula {Volume} = {2}\{3}pi (216 - 64)$ {Volume} = {2}\{3}pi (152)
Step 4: Final calculation {Volume} = 2 times 152 pi}\{3}
{Volume} = 304\pi\{3}\ cm}^3
Final Result:
The volume of the solid part in the hemisphere shell is 304π/3 cm³
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
