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Question
In the given figure, a toy made from a hemisphere, a cylinder and a cone are shown. Find the total area of the toy.
Solution
Radius of the sphere = Radius of the cylinder = Radius of cone = r = 3 cm
Height of the cone, h = 4 cm
Height of the cylinder, H = 40 cm
Let the slant height of the cone be l cm.
l2 = r2 + h2
= 32 +42
= 9 + 16
= 25
l = `sqrt25`
∴ l = 5 cm
Total area of the toy = Curved surface area of hemisphere + Curved surface area of cylinder + Curved surface area of cone
\[= 2\pi r^2 + 2 \pi rH + \pi rl\]
\[ = 2\pi \times \left( 3 \right)^2 + 2\pi \times 3 \times 40 + \pi \times 3 \times 5\]
= 2π × 9 + 240π + 15π
= 18π + 240π + 15π
= 273π cm2
Thus, the total area of the toy is 273π cm2.
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