A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 32 cm. Find its TSA

Hi Ishwaryaa,
Please find below the solution to the asked query :

 


Let r be the radius of the base of cylinder and h be the height of the cylinder.Now, r  = 28 mm = 2.8 cm ; h = 9.6 cmNow, when a cone of same base radius and same height is removed from a solid cylinder, then volume of remaining solid = volume of cylinder - volume of cone= πr2h - 13πr2h=23πr2h =23π × 7.84 × 9.6= 157.696 cm3Now,TSA of remaining solid = CSA of cylinder + CSA of cone + area of  1 base of cylinder=2πrh + πrr2+h2 + πr2=πr2h + r2+h2 + r=2.8π2×9.6 + 2.82+9.62 + 2.8=6π19.2 + 10 + 2.8=12π32=12×227×32=1206.86 cm2=12 × 3.14 × 18.83=709.51 cm2
 

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