Q. 124.0( 4 Votes )

# A toy is in the form of a cone mounted on a hemisphere on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. find the total surface area of the toy.

Answer :

Given: Height of toy = h = 31 cm

Radius of hemisphere = radius of base of cone = r = 7 cm

From the figure we can calculate height of cone as

Height of cone = h_{c} = h - r

= 31 - 7 = 24 cm

∴ h_{c} = 24 cm

Formula: surface area of hemisphere = surface area of sphere/2 = 2πr^{2}

Curved surface area of cone = πrl

Where l is slant height

l = √(49 + 576) = 25 cm

∴ l = 25 cm

Total surface area of toy = curved surface area of cone + surface area of hemisphere

Surface area of hemisphere = 2 × π × r^{2}

= 2 × (22/7) × 7^{2}

= 308 cm^{2}

Curved surface area of cone = π × r × l

= (22/7) × 7 × 25

= 550 cm^{2}

∴ Total surface area of toy = 308 + 550

= 858 cm^{2}

∴ Total surface area of toy = 858 cm^{2}

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