Question

If the height of a right prism is increased by 50% and base area remains the same, what is the percentage increase in volume?

• A. 25%
• B. 50%
• C. 75%
• D. 100%

Answer 1

Answer:

B. 50%

Volume of a right prism:

$V = \text{Base Area} \times \text{Height}$

Let original height = (h), base area = (A)

Original volume:
$V_1 = Ah$

Step 1: New height

Increased by 50%:
$h' = 1.5h$

Step 2: New volume

$V_2 = A \times 1.5h = 1.5Ah$

Step 3: Increase in volume

$V_2 - V_1 = 1.5Ah - Ah = 0.5Ah$

Step 4: Percentage increase

$\frac{0.5Ah}{Ah} \times 100 = 50\%$

Final Answer:

$\boxed{50\%}$