Maths question from Laboratory Attendant exam, 2026 by JKSSB
A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edges of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volume of the cube is 343 cc, what approximately is the volume of the cone?
Last updated Jun 13, 2026
Correct Answer:
Option C —
90 cc
Step-by-Step Breakdown:
Find the dimensions of the cube:
The volume of a cube is calculated by cubing its side length. We are given that the volume is 343 cubic centimeters.
Since 7 multiplied by 7 multiplied by 7 equals 343, the side length of the cube is exactly 7 centimeters.
Relate the cube to the cone:
Height of the cone: The vertex of the cone touches the opposite face of the cube, meaning the height of the cone is equal to the side length of the cube. So, the height is 7 centimeters.
Diameter of the cone's base: The base of the cone touches the edges of one face of the cube perfectly. This means the diameter of the circular base is also equal to the side length of the cube, which is 7 centimeters.
Radius of the cone's base: The radius is half of the diameter, which is 7 divided by 2, or 3.5 centimeters.
Calculate the volume of the cone:
The formula for the volume of a cone is one-third multiplied by pi multiplied by the radius squared multiplied by the height.
Let's use 22 divided by 7 as an approximate value for pi.
The radius squared is 3.5 multiplied by 3.5, which equals 12.25.
Now, multiply the parts together: one-third multiplied by (22 divided by 7) multiplied by 12.25 multiplied by 7.
The 7 in the numerator and the 7 in the denominator cancel each other out.
This leaves us with: one-third multiplied by 22 multiplied by 12.25.
22 multiplied by 12.25 equals 269.5.
Finally, divide 269.5 by 3, which equals approximately 89.83 cubic centimeters.
Match with the options:
Rounding 89.83 cubic centimeters to the nearest whole number gives us 90 cubic centimeters.
Answer verified by Quintessence Classes faculty — Karan Nagar, Srinagar.
