1) The area of CSA (in sq cm) of a cylinder is numerically equal to its volume (in cc). Find the area of cylinder ?
2) The area of WSA of a solid sphere and solid hemisphere are equal. Find the ratio of their radius ?
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Answer 1) :-
Given,
→ CSA of cylinder = Volume of cylinder .
Let us assume that,
- radius of cylinder = r cm .
- height of cylinder = h cm.
then, A/q,
→ 2 * π * r * h = π * r² * h
→ 2 = r .
therefore, we can conclude that , if r = 2 cm, for all values of h , CSA of cylinder will be equal to volume of cylinder.
Hence,
→ Total area of cylinder = 2πr(h + r) = 2π*2(h + 2) = 4π(h + 2) cm² (Ans.)
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Answer 2) :-
Let us assume that, radius of Solid sphere is R cm and radius of Solid hemisphere is r cm.
then,
→ TSA of sphere = TSA of hemisphere .
→ 4π(R)² = 3π*(r)²
→ 4R² = 3r²
→ R²/r² = 3/4
→ (R/r)² = 3/4
→ R/r = √3/2
→ R : r = √3 : 2 . (Ans.)
Therefore, ratio of radius of Solid sphere is to radius of Solid hemisphere is √3 : 2 .
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