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.
The toy is in the form of a cone mounted on a hemisphere.
Total height of toy = h = 31 cm
Radius of toy = r = 7 cm
Surface area of hemispherical part toy = 2πr2
= 2 × 22/7 × 72 cm2
= 308 cm2
Height of conical part of toy = hcone = Total height of toy – Radius of toy
Height of conical part of toy = hcone = 31 – 7 = 24 cm
Let the slant height of the conical part be l
l2 = hcone2 + r2
l2 = 242 + 72 = 576 + 49 cm2 = 625 cm2
l = 25 cm
Surface area of conical part of toy = πrl
= 22/7 × 7 × 25 cm2
= 550 cm2
Total surface area of toy = Surface area of hemispherical part of toy + Surface area of conical part of toy
Total Surface area of toy = 308 cm2 + 550 cm2 = 858 cm2