Q. 304.5( 12 Votes )

Answer :

The toy is in the shape of a right circular cylinder surmounted by a cone at one end a hemisphere at the other.

Total height of toy = 30 cm

Height of cylinder = h = 13 cm

Radius of cylinder = r = 5 cm

Curved surface area of cylinder = 2πrh

= 2 × 22/7 × 5 × 13 cm^{2}

Height of cone = h’ = Total height of toy – Height of cylinder – Radius of hemisphere

Height of cone = h’ = 30 cm – 13 cm – 5 cm = 12 cm

Radius of cone = r = Radius of cylinder

Radius of cone = r = 5 cm

Let the slant height of cone be l

l^{2} = h’^{2} + r^{2}

⇒ l^{2} = 12^{2} + 5^{2} cm^{2} = 144 + 25 cm^{2} = 169 cm^{2}

⇒ l = 13 cm

Curved surface area of cone = πrl

= 22/7 × 5 × 13 cm^{2}

Radius of hemisphere = r = Radius of cylinder

Radius of hemisphere = r = 5 cm

Curved surface area of hemisphere = 2πr^{2}

= 2 × 22/7 × 5 × 5 cm^{2}

Surface area of the toy = Surface area of cylinder + Surface area of cone + Surface area of hemisphere

Surface area of toy = 2πrh + πrl + 2πr^{2}

= πr (2h + l + 2r)

= 22/7 × 5 × (2 × 13 + 13 + 2 × 5) cm^{2}

= 22/7 × 5 × 49 cm^{2}

= 770 cm^{2}

Surface area of toy is 770 cm^{2}

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