Question
Download Solution PDFएक समकोणीय पिरामिड का आधार
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया हैं:
एक समकोण पिरामिड का आधार
तिरछे किनारे की लंबाई = 10 सेमी
प्रयुक्त सूत्र:
पिरामिड का आयतन = (आधार का क्षेत्रफल × ऊँचाई)/3
गणना:
माना OABCD वर्गाकार आधार का एक समकोण पिरामिड है।
माना [OP = h] पिरामिड की ऊँचाई है।
ऊँचाई OP ज्ञात करने के लिए सबसे पहले हमें DP ज्ञात करना होगा
DP = वर्ग के विकर्ण का आधा
⇒ DP = (1/2) × [√2 × 8√2] = 8 सेमी
अब, समकोण त्रिभुज में OPD
OP2 = OD2 - DP2 [∠OPD = 90°]
⇒ OP2 = 102 - 82 = 62
⇒ OP = 6
⇒ पिरामिड की ऊँचाई = 6 सेमी
अब, पिरामिड का आयतन = (1/3) × आधार का क्षेत्रफल × 6
⇒ (1/3) × (8√2)2 × 6
⇒ 256 सेमी3
∴ पिरामिड का आयतन 256 सेमी3 है।
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