Question

Find the surface area of the figure in squared meters.

Answer 1

The surface area of a cone is given by the equation

$A=\pi r(r+\sqrt[]{r^2+h^2})$

where r is the radius of the base and h is the height of the cone.

Now in our case, we are not given the height h, rather, we are given the length of the diagonal. We can, however, use the Pythagoras's theroem to find the height.

$17^2=(7.2)^2+h^2$

Subtracting 7.2^2 from both sides gives

$\begin{gathered} h^2=17^2-7.2^2 \\ h=\sqrt[]{17^2-7.2^2} \\ h=15.4 \end{gathered}$

Now that we know the height of the cone, we can now use the formula for the area of the cone.

$A=\pi(7.2m)((7.2m)+\sqrt[]{(7.2)^2+(15.4)^2})$$\boxed{A=547.39\: m^3\text{.}}$

Hence, the correct answer is the top second choice.