a right circular cone of vertical height 24cm has volume 616 cm cube find the area of its curved surface
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a right circular cone of vertical height , h = 24cm
volume of the right circular cone , V = 616cm³
we know, volume of cone = πr²h/3
so, 616 = 22/7 × r² × 24/3
or, 616 × 7 = 22 × 8 × r²
or, 56 × 7 = 2 × 8 × r²
or, r² = 7 × 7/2 = 49/2
or, r = 7/√2
slant height, l = √(r² + h²) = √(49/2 + 576)
l = √(600.5)
so, curved surface area of cone = πrl
= 22/7 × 7/√2 × √(600.5)
= 22 × √(300.25)
= 381.2cm²
volume of the right circular cone , V = 616cm³
we know, volume of cone = πr²h/3
so, 616 = 22/7 × r² × 24/3
or, 616 × 7 = 22 × 8 × r²
or, 56 × 7 = 2 × 8 × r²
or, r² = 7 × 7/2 = 49/2
or, r = 7/√2
slant height, l = √(r² + h²) = √(49/2 + 576)
l = √(600.5)
so, curved surface area of cone = πrl
= 22/7 × 7/√2 × √(600.5)
= 22 × √(300.25)
= 381.2cm²
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