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Question
A wooden toy is in the shape of a cone mounted on a cylinder as shown alongside. If the height of the cone is 24 cm, the total height of the toy is 60 cm and the radius of the base of the cone = twice the radius of the base of the cylinder = 10 cm; find the total surface area of the toy. [Take π = 3.14]
Solution
Height of the cone = 24 cm
Height of the cylinder = 36 cm
Radius of the cone = twice the radius of the cylinder = 10 cm
Radius of the cylinder = 5 cm
Slant height of the cone = `sqrt(r^2 + h^2)`
= `sqrt(10^2 + 24^2)`
= `sqrt(100 + 576)`
= `sqrt(676)`
= 26 cm
Now, the surface area of the toy = curved area of the conical point + curved area of the cylinder
= πrl + πr2 + 2πRH
= π[rl + r2 + 2RH]
= 3.14[10 × 26 × (10)2 + 2 × 5 × 36]
= 3.14[260 + 100 + 360]
= 3.14[720]
= 2260.8 cm2
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