Question

A toy is in the form of a cone mounted on a hemisphere of common base of radius 7cm. The total height of the toy is 31 cm. Find the total surface area of the toy.

Answer 1

Since, total height of the toy is 31 cm. 

But given that conical part is mounted on a hemisphere of radius 7 cm.

∴ The height of the cone is h = 31 – 7 = 24 cm.

And radius of cone is r = 7cm.

∴ The slant height of the cone is l = \(\sqrt{r^2+h^2}=\sqrt{7^2+24^2}=\sqrt{49+576}\)

\(=\sqrt{625}\) =  25 cm.

Now, total surface area of toy = surface area of hemisphere + surface area of cone.

= \(2\pi r^2+\pi r(2\pi+l)\)

= \(\frac{22}{7}\times7(2\times7+25)\) = \(22\times(14+25)=22\times39=858\) = cm².

Hence, the total surface area of the toy is 858 cm².