Question

The radius of a right circular cone is increased by 50%, then its volume increases by ..........

• A. 125%
• B. 100%
• C. 237.5%
• D. 75%

Hint:

When dealing with geometric shapes, remember that volume changes with the cube of the scaling factor for three-dimensional objects.

Answer 1

The Correct Option is A

The volume \( V \) of a right circular cone is given by the formula: \[ V = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius and \( h \) is the height. If the radius is increased by 50%, the new radius becomes \( 1.5r \). Since the volume depends on the square of the radius, the new volume becomes: \[ V' = \frac{1}{3} \pi (1.5r)^2 h = \frac{1}{3} \pi .2.25r^2 h = 2.25V \] Thus, the volume increases by 125%, as \( 2.25V - V = 1.25V \).

Answer 2

The volume of a right circular cone is given by the formula:
V = (1/3) × π × r² × h
where r is the radius and h is the height.

Step 1: Original Volume
Let the original radius = r and height = h
Original volume = (1/3) × π × r² × h

Step 2: New radius after 50% increase
New radius = r + 50% of r = 1.5r
Height remains unchanged.

New volume = (1/3) × π × (1.5r)² × h
= (1/3) × π × 2.25r² × h
= 2.25 × (1/3) × π × r² × h

Step 3: Compare new volume with original
New volume = 2.25 × original volume
Increase in volume = (2.25 - 1) × 100% = 1.25 × 100% = 125%

Conclusion:
When the radius of a right circular cone is increased by 50%, its volume increases by 125%.