Question

a toy is in the form of a cone mounted on a hemisphere of same radius 7 cm if the total height of the toy is 31 cm find its total surface area

Answer 1

Radius of hemisphere = 7
Height of hemisphere = 7 (height and radius of hemisphere are equal)
Total height of toy = 31

Height of cone = 31-7 = 24 cm.
Slant height of cone = √(24)² + (7)²
√576 + 49 = √625 = 25cm

Total surface area of toy = TSA of cone + TSA of hemisphere
πr (l+r) + 3πr²
22/7 (25 + 7) + 3× 22/7 (7)²
704/7 + 462
100.57 + 462 = 562.57
Total surface area of toy = 562.57

Answer 2

l²=r²+h²⇒l=√r²+h²=√7²+31² cm=√49+961 cm=√1010 cm=31.78cm(approx.)
Total surface area of the toy=πr(l+r)sq.units
=22/7×7×(31.78+7)cm²
=22/7×7×38.78=853.16cm²(approx.)