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  • A solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is 10 cm and the radius of the base is 7 cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cov

A solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is 10 cm and the radius of the base is 7 cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cover the toy.  \dpi{100} (\: U\! se\: \pi = \frac{22}{7} \: and\: \sqrt{149}=12.2)
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Answers (1)

\\ $Given: height of the cone (h) = 10 cm, radius of the base(r) = 7 cm $ \\ \text {Volume of toy = Volume of hemisphere + volume of the cone} \\ =\frac{2}{3} \pi(r)^{3}+\frac{1}{3} \pi(r)^{2} \times h \ \mathrm{cm}^{3} \\ =\frac{2}{3} \pi(7)^{3}+\frac{1}{3} \pi(7)^{2} \times 10 \ \mathrm{cm}^{3} \\ =\frac{1}{3} \times \frac{22}{7} \times 49 (14+10) \\ =22 \times 7 \times 8 \\ =1232 \mathrm{cm}^{3} \\ \text { Area of Sheet } =\text { Surface area of the toy} \\ =2 \pi(r)^{2}+\pi(r) (l) \\=2 \pi(7)^{2}+\pi(7) \sqrt{10^{2}+7^{2}} \\ =308+22 \times 12.2\\=576.4 \mathrm{cm}^{2}

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