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Letâ€™s start everything with making a figure of what the question says.

So, from the above figure it is clear that the total surface area of the toy which is exposed to us is the curved surface area of a cone and curved surface area of the hemisphere.

$ \Rightarrow $ The total surface area of the toy$ = $ Curved surface area of cone$ + $ Curved surface area of hemisphere

Given the question that, radius$\left( r \right)$ of cone and hemisphere is $3.5cm$and the total height of toy, i.e. height of cone$ + $ Radius of the hemisphere is $15.5cm$.

Height of the cone$\left( h \right) = 15.5 - 3.5 = 12cm$

We know that the formula for the curved surface area of the cone is $\pi $ times radius times slant height, i.e. $\pi r\sqrt {{r^2} + {h^2}} $ and for the hemisphere, the formula is twice the radius square times $\pi $, i.e. $2\pi {r^2}$

With these formulas, the above relation can be written as

The total surface area of the toy $ = \pi r\sqrt {{r^2} + {h^2}} + 2\pi {r^2}$

Let us now substitute the known values in the equation

The total surface area of the toy $ = \pi \times 3.5 \times \sqrt {{{3.5}^2} + {{12}^2}} + 2 \times \pi \times {3.5^2}$

Solving this equation with the value of $\pi = 3.141$

The total surface area of the toy$ = 3.14 \times 3.5 \times \sqrt {12.25 + 144} + (2 \times 3.14 \times 12.25)$

On solving it further, youâ€™ll get

The total surface area of the toy$ = 10.99 \times \sqrt {156.25} + (2 \times 38.465) \Rightarrow 10.99 \times 12.5 + 76.93 \Rightarrow 137.375 + 76.93 \Rightarrow 214.3c{m^2}$.