Question
Download Solution PDF10 सेमी बाजू असलेल्या एका चौरसाकृती पिरॅमिडचे घनफळ 400 सेमी3 आहे. पिरॅमिडचे एकूण पृष्ठफळ शोधा.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिलेले आहे:
10 सेमी बाजू असलेल्या एका चौरसाकृती पिरॅमिडचे घनफळ 400 सेमी3 आहे.
वापरलेले सूत्र:
पिरॅमिडचे घनफळ = 1/3 × पायाचे क्षेत्रफळ × उंची
एकूण पृष्ठफळ = पायाचे क्षेत्रफळ + चौरसाकृती पिरॅमिडचे पार्श्व पृष्ठफळ
पार्श्व पृष्ठफळ = 1/2 × पायाची परिमिती × तिरपी उंची
गणना:
पिरॅमिडच्या पायाचे क्षेत्रफळ = चौरसाचे क्षेत्रफळ = (10)2 = 100 सेमी2
पिरॅमिडचे घनफळ = 1/3 × पायाचे क्षेत्रफळ × उंची
⇒ 400 = 1/3 × 100 × उंची
⇒ पिरॅमिडची उंची = 12 सेमी
⇒ पिरॅमिडची तिरपी उंची = √[(उंची)2 + (बाजू/2)2]
⇒√(144 + 25) = √169 = 13 सेमी
पार्श्व पृष्ठफळ = 1/2 × 4 × 10 × 13 = 260 सेमी2
एकूण पृष्ठफळ = 100 सेमी2 + 260 सेमी2 = 360 सेमी2
∴ 360 सेमी2 हे योग्य उत्तर आहे.
Last updated on Jul 17, 2025
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