Question

A right circular cone of volume $A$, a right circular cylinder of volume $M$, and a sphere of volume $C$ all have the same radius, and the common height of the cone and the cylinder is equal to the diameter of the sphere. Then

• A. $A-M+C=0$
• B. $A+M=C$
• C. $2A=M+C$
• D. $A^2-M^2+C^2=0$

Answer 1

Answer: (A)

$A-M+C=0$

A right circular cone , a right circular cylinder and a sphere have same radius (say r ) and heights of cone and cylinder are equal to diameter of sphere $(=2r)$

So, Volume of cone = $\frac{1}{3}\pi r^{2}h$

$A=\frac{1}{3}\pi r^2\times 2r$

$A=\frac{2}{3}\pi r^3$

Similarly , volume of cylinder$=M=2\pi r^3$

and volume of sphere $=C=\frac{4}{3}\pi r^3$

Clearly , $A+C-M=0$ Hence option $A$.