The length, breadth and height of a cuboid are in the ratio 2 : 3 : 6 and its diagonal is 21 cm. Find its volume.
एक घनाभ (Cuboid) की लंबाई, चौड़ाई और ऊँचाई का अनुपात (Ratio) 2 : 3 : 6 है और इसका विकर्ण (Diagonal) 21 cm है। इसका आयतन (Volume) ज्ञात कीजिए।
Answer और ExplanationAnswer and explanation
Answer: (C) 972 cm³
मान लें l = 2k, b = 3k, h = 6k है।
विकर्ण (Diagonal) = k√(4 + 9 + 36) = k√49 = 7k = 21 ⇒ k = 3
तो l = 6 cm, b = 9 cm, h = 18 cm
आयतन (Volume) = 6 × 9 × 18 = 972 cm³
✓
घनाभ (Cuboid) का आयतन 972 cm³ है।
Let l = 2k, b = 3k, h = 6k.
Diagonal = k√(4 + 9 + 36) = k√49 = 7k = 21 ⇒ k = 3
So l = 6 cm, b = 9 cm, h = 18 cm
Volume = 6 × 9 × 18 = 972 cm³
✓
The volume is 972 cm³.
SMART APPROACH
7k = 21 से k = 3 मिलते ही आयतन (Volume) = (2 × 3 × 6)k³ = 36 × 27 = 972 cm³।
Volume = (2 × 3 × 6)k³ = 36 × 27 = 972 cm³, once 7k = 21 gives k = 3.
Source: Selection Post Phase XIV (12th) · 16 Sep 2026 · Shift 2। Solution: Prashant Sir, Vijayastra।Source: Selection Post Phase XIV (12th) · 16 Sep 2026 · Shift 2. Solution by Prashant Sir, from Vijayastra.