Question

the area of the base of a conical solid is 38.5 CM square and its volume is 154 centimetre cube find the Curved surface area of the solid

Answer 1

Heya !!!





Area of base of conical solid = 38.5 cm



πR² = 38.5




22/7 × R² = 38.5





R² = 38.5 × 7 /22




R² => 12.25 cm



R = ✓12.25 = 3.5 m




Volume of conical solid = 154




1/3 πR² H = 154





1/3 × 22/7 × 3.5 × 3.5 × H = 154




H = 154 × 21 / 22 × 3.5 × 3.5




H = 3234/269.5




H = 12 m






Slant height ( L ) = ✓ ( R)² + (H)²




=> ✓ ( 3.5)² + (12)²



=> ✓12.25 + 144




=> ✓ 156.25



=> 12.5 cm



Therefore,




CSA of solid = πRL




=> 22/7 × 3.5 × 12.5





=> 137.5 cm².




★ HOPE IT WILL HELP YOU ★

Answer 2

hii!!

here's Ur answer...

given the area of the base of the conical solid us given 38.5cm²

we know that the base of a cone is circular.

therefore πr² = 38.5cm²

==> 22/7 × r² = 38.5cm²

==> r² = 38.5/1 × 7/22

==> r² = 269.5/22

==> r² = 12.25

==> r = 3.5cm

hence, the radius of the base of the conical solid is 3.5cm.

volume of the conical solid = 154cm³

therefore 1/3πr²h = 154cm³

==> 1/3 × 22/7 × 3.5 × 3.5 × h = 154cm³

==> 22/6 × 3.5 × h = 154cm³

==> 77/6 × h = 154cm³

==> h = 154/1 × 6/77

==> h = 924/77

==> h = 12cm

now, we have to find the CSA (curved surface area) of the conical solid. and formula for finding it's CSA is πrl where length is the slant height.

so now we have to find it's slant height.

by Pythagoras thereom :-

l = slant height, r = radius and h = height

l² = r² + h²

l² = 3.5² + 12²

l² = 12.25 + 144

l² = 156.25

l = √156.25

l = 12.5cm

slant height of the conical solid is 12.5cm

CSA of the conical solid = πrl

= 22/7 × 3.5 × 12.5

= 962.5/7

= 137.5cm²

hope this helps..!!