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A toy is in the form of a cone mounted on a hemisphere of radius $7$ cm. The total height of the toy is $31$ cm. Find the total surface area of the toy.
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Sol. Height of conical part $= 31 – 7 = 24$ cm
Slant height of conical part $= \sqrt{(7)^2 + (24)^2} = 25$ cm (1/2 Mark)
TSA of the toy = CSA of conical part + CSA of hemispherical part (1 Mark)
$= 2\pi r l + 2\pi r^2 = 2 \times \frac{22}{7} \times 7 \times 25 + 2 \times \frac{22}{7} \times 7 \times 7$ (1 Mark)
$= 858$ cm$^2$ (1/2 Mark)
So, the total surface area of the toy is $858$ cm$^2$.
Slant height of conical part $= \sqrt{(7)^2 + (24)^2} = 25$ cm (1/2 Mark)
TSA of the toy = CSA of conical part + CSA of hemispherical part (1 Mark)
$= 2\pi r l + 2\pi r^2 = 2 \times \frac{22}{7} \times 7 \times 25 + 2 \times \frac{22}{7} \times 7 \times 7$ (1 Mark)
$= 858$ cm$^2$ (1/2 Mark)
So, the total surface area of the toy is $858$ cm$^2$.