A triangular prism has base area of 25 cm². If height is increased by 20%, what is the new volume (original height was 10 cm)?

Question

A triangular prism has base area of 25 cm². If height is increased by 20%, what is the new volume (original height was 10 cm)?

1. A. 250 cm³
2. B. 275 cm³
3. C. 300 cm³ (Correct answer)
4. D. 225 cm³

Correct Answer

Option C — 300 cm³

Detailed Solution & Explanation

The correct answer is 300 cm³.

Key Points

• The volume of any prism is base area × height, whatever the shape of the base.
• Original volume = 25 × 10 = 250 cm³.
• The height rises by 20%: 10 × 1.2 = 12 cm.
• New volume = 25 × 12 = 300 cm³.
• Because the base area is unchanged, volume scales in direct proportion to height — 250 × 1.2 = 300 gets there in one step.
• Only one dimension changes here; had all three been scaled by 20%, the volume would have risen by a factor of 1.2³ = 1.728, not 1.2.

Additional Information

• Volume of a prism = base area × height, whatever the base shape; the same rule covers cuboids, triangular prisms and cylinders.
• Scaling one dimension scales the volume in direct proportion; scaling all three by k multiplies the volume by k³ and the surface area by k².
• A 20% increase means multiplying by 1.2 — adding 20% of the original is the same thing here, but the multiplier form is safer in multi-step questions.

प्रश्न (हिन्दी में)

एक त्रिभुजाकार प्रिज्म का आधार क्षेत्रफल 25 वर्ग सेमी है। यदि ऊँचाई 20% बढ़ा दी जाए, तो नया आयतन क्या होगा (मूल ऊँचाई 10 सेमी थी)?

1. A. 250 सेमी³
2. B. 275 सेमी³
3. C. 300 सेमी³
4. D. 225 सेमी³