Maths question from Laboratory Attendant exam, 2026 by JKSSB
Two metallic right circular cones having their heights 3.8 cm and 4.6 cm and radii of their bases 2.1 cm each, have been melted together and recast into a sphere. The diameter (in cm) of the sphere is:
Last updated Jun 19, 2026
Correct Answer:
Option A —
4.2
To find the diameter of the sphere, we can look at the total volume of the metal being melted and recast. When the two cones are melted together, their combined volume is exactly equal to the volume of the new sphere.
Step 1: Understand the Volume of the Cones
The volume of a cone is calculated as one-third times pi times the radius times the radius times the height.
Since both cones have the same base radius of 2.1 cm, we can combine their volumes by adding their heights together.
The height of the first cone is 3.8 cm.
The height of the second cone is 4.6 cm.
Adding the heights together gives 8.4 cm.
Now, we can find the total volume of both cones combined:
Total volume equals one-third times pi times 2.1 times 2.1 times 8.4.
Dividing 8.4 by 3 gives 2.8.
So, the total volume simplifies to pi times 2.1 times 2.1 times 2.8.
This works out to pi times 12.348 cubic cm.
Step 2: Find the Radius of the Sphere
The volume of a sphere is calculated as four-thirds times pi times the radius times the radius times the radius (the radius cubed).
Since the volume of the sphere is equal to the total volume of the cones:
Four-thirds times pi times the radius cubed equals pi times 12.348.
We can remove pi from both sides of the comparison:
Four-thirds times the radius cubed equals 12.348.
To find the radius cubed, we multiply 12.348 by 3 and then divide by 4:
Radius cubed equals 37.044 divided by 4.
Radius cubed equals 9.261.
To find the radius itself, we look for a number that, when multiplied by itself three times, equals 9.261.
The cube root of 9.261 is 2.1.
So, the radius of the sphere is 2.1 cm.
Step 3: Find the Diameter of the Sphere
The diameter of a sphere is always twice its radius.
Diameter equals 2.1 times 2.
Diameter equals 4.2 cm.
Correct Answer:
A) 4.2
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
