12 सेंटीमीटर त्रिज्या 10 सेंटीमीटर ऊंचाई वाले लंब वृत्तीय बेलन का संपूर्ण पृष्ठ ज्ञात कीजिए
Answers
Given:
A cube can be inscribed cylinder of radius 5 cm and height 12 cm.
To Find:
What is the total surface area of largest cube ?
Solution:
Radius of cylinder (R) = 5 cm
Diameter of cylinder (D) = 10 cm
It is clear that diagonal of face of cube will be diameter of cylinder:
Diagonal of face of cube = 10 cm
So side of cube:
Side² + Side² = Diagonal²
2×Side² = Diagonal²
On putting respective value in above equation:
2×Side² = 10²
2×Side² = 100
Side² = 50 ...1)
Side = √50
Means side of cube = √50 cm
√50 < 12
√50 < height of cylinder
So √50 is largest side of cube:
Total surface area of cube will be:
Total surface are = 6× Side²
From equation 1):
Total surface are = 6× 50
Total surface are = 300 cm²
So total surface area of largest cube which can be inscribed cylinder of radius 5 cm and height 12 cm is 300 cm².
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