Question

Kritika has three solid objects cone, hemisphere, cylinder. All have same base radius and height. Then the ratio of volume of cylinder : cone : hemisphere is

• A. \(1:2:3\)
• B. \(1:1:1\)
• C. \(3:1:2\)
• D. \(2:1:3\)

Hint:

Remember: \[ \text{Cylinder : Cone} = 3:1 \] for equal radius and height.

Answer 1

The Correct Option is C

Concept: Volume formulas: Cylinder: \[ V_c=\pi r^2 h \] Cone: \[ V_{cone}=\frac13\pi r^2 h \] Hemisphere: \[ V_h=\frac23\pi r^3 \] Given same radius and height. For hemisphere, height equals radius. Thus \[ h=r \]

Step 1: Substitute \(h=r\). Cylinder: \[ V_c=\pi r^3 \] Cone: \[ V_{cone}=\frac13\pi r^3 \] Hemisphere: \[ V_h=\frac23\pi r^3 \]

Step 2: Find ratio. \[ \pi r^3: \frac13\pi r^3: \frac23\pi r^3 \] Multiplying by 3: \[ 3:1:2 \] Hence, \[ \boxed{3:1:2} \] \[ \boxed{\text{Answer = (C)}} \]