Question
Download Solution PDFएक लंबकोणीय प्रिज्म का आधार 5 cm भुजा वाला एक समषट्भुज है। यदि इसकी ऊँचाई 12√3 cm है, तो इसका आयतन (cm3 में) ज्ञात कीजिए।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है :-
एक लंबवत प्रिज्म का आधार, 5 cm भुजा का एक नियमित षट्भुज है
ऊँचाई 12√3 cm है
अवधारणा :-
प्रिज्म, बेलन का एक भाग है, इसलिए -
प्रिज्म का आयतन = आधार × ऊँचाई
प्रिज्म का आधार षट्भुज है,
षट्भुज आधार के साथ प्रिज्म का आयतन = आधार का क्षेत्रफल × ऊँचाई
आधार का क्षेत्रफल = षट्भुज का क्षेत्रफल, 6 समबाहु त्रिभुज के क्षेत्रफल के बराबर है = 6 × (√3/4) × भुजा2
गणना :-
⇒ आधार का क्षेत्रफल = 6 × (√3/4) × 52
⇒ आधार का क्षेत्रफल = 150 × (√3/4)
⇒ आयतन = 150 × (√3/4) × 12√3
⇒ आयतन = (1800 × 3)/4
⇒ आयतन = 1350 cm3
∴ आयतन = 1350 cm3
Last updated on Jun 13, 2025
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