Area of base of a cone solid is 38.5 cm square
Answers
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