Question

A cone of height 24cm has a curved surface are 550 cm^2 .find its radius

Answer 1

Curved Surface area of a Cone = pi r L, where r is the radius of the base & L is its slant height.Height(h) of the cone = 24cm.So, in right triangle slant height L= √( h² + r²) = √(24² + r²)= √(576+r²)Pi r L = 550=> pi * r * (√(24² + r²) = 550=> pi² * r² * ( 24² + r²) = 550² ( On squaring)=> 576pi²r² + pi²r^4 = 550²=> pi² r^4 + 576pi² r² - 550² =0Let r² be x=> pi²x² + 576pi²x - 550² =0=> 22/7 *22/7 *x² + 576*22/7*22/7 -2²*5²*5²*11²= 0 Now divide each term by 11²=> 4/49x² + 576*4/49 *x - 2500=0= 4x² + 2304x - 122500 =0 ( by multiplying each term by 49)=> x² + 576x - 30625 = 0=> x = (-576 +,-√454276)/2x = (-576 + 674)/2 ( -ve value is ruled out)=> x = 98/2 = 49=> r² = 49=> r = 7So, Volume of Cone = 1/3* pi* r² * h=> Volm = 1/3 * 22/7 * 7*7*24= Volm = 22*7*8=> 1232 cu cm ………ANS.