Q. 324.9( 9 Votes )

# A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part in 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of them colours. [Take π = 22/7.]

Answer :

The wooden toy is in the shape of a cone mounted on a cylinder

Total height of the toy = 26 cm

Height of conical part = H = 6 cm

Height of cylindrical part = Total height of the toy – Height of conical part

h = 26 cm – 6 cm = 20 cm

Diameter of conical part = 5 cm

Radius of conical part = R = Diameter/2 = 5/2 cm = 2.5 cm

Let L be the slant height of the cone

L^{2} = H^{2} + R^{2}

⇒ L^{2} = 6^{2} + 2.5^{2} cm^{2} = 36 + 6.25 cm^{2} = 42.25 cm^{2}

⇒ L = 6.5 cm

Diameter of cylindrical part = 4 cm

Radius of cylindrical part = r = Diameter/2 = 4/2 cm = 2 cm

Area to be painted Red = Curved Surface area of cone + Base area of cone – base area of cylinder

Area to be painted Red = πRL + πR^{2} – πr^{2} = π (RL + R^{2} – r^{2})

= 22/7 × (2.5 × 6.5 + 2.5 × 2.5 – 2 × 2) cm^{2}

= 22/7 × (16.25 + 6.25 – 4) cm^{2}

= 22/7 × 18.5 cm^{2}

= 58.143 cm^{2}

Area to be painted White = Curved Surface area of cylinder + Base area of cylinder

Area to be painted White = 2πrh + πr^{2} = πr (2h + r)

= 22/7 × 2 × (2 × 20 + 2) cm^{2}

= 22/7 × 2 × (40 + 2) cm^{2}

= 22/7 × 2 × 42 cm^{2} = 264 cm^{2}

∴ Area to be painted red is 58.143 cm^{2} and area to be painted white is 264 cm^{2}.

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