The total surface area of a right circular cone of slant height $20 c m$ is $384 π c m^{2}$ .
Calculate: (i) its radius in $c m$ ;
(ii) its volume in $c m^{3}$ , in terms of $π$ .

Question

The total surface area of a right circular cone of slant height 20 -cm is 384 -pi -cm-2-Calculate- -i- its radius in cm- -ii- its volume in cm-3- in terms of pi-

Toppr Admin · Accepted Answer

T-S-A- -x3C0-r2-x3C0-rl-384-x3C0-xA0-cm2-x27F9-x3C0-r2-r-xD7-20-384-x3C0-x27F9-r2-20r-x2212-384-0-x27F9-r-12-x2212-32Considering the value r-12-xA0-cm-xA0- as radius cannot be negative-Volume -x3C0-3r2h-x3C0-3-xD7-122-xD7-16-2412-7-xA0-cm3

The total surface area of a right circular cone of slant height 20cm is 384πcm2.Calculate: (i) its radius in cm; (ii) its volume in cm3, in terms of π.

T.S.A. =πr2+πrl=384π cm2⟹π(r2+r×20)=384π⟹r2+20r−384=0⟹r=12,−32Considering the value r=12 cm as radius cannot be negative.Volume =π3r2h=π3×122×16=2412.7 cm3

The total surface area of a right circular cone of slant height $20 c m$ is $384 π c m^{2}$ .
Calculate: (i) its radius in $c m$ ;
(ii) its volume in $c m^{3}$ , in terms of $π$ .

T.S.A. $= π r^{2} + π r l = 384 π {cm}^{2}$
$⟹ π (r^{2} + r \times 20) = 384 π$
$⟹ r^{2} + 20 r - 384 = 0$
$⟹ r = 12, - 32$

Considering the value $r = 12 cm$ as radius cannot be negative.

Volume $= \frac{π}{3} r^{2} h$
$= \frac{π}{3} \times 12^{2} \times 16$
$= 2412.7 {cm}^{3}$