Question

Find the total surface area of this cone. Round to the nearest tenth.

Answer 1

Step-by-step explanation:

for given cone:

h = 3 ft, r = 3 ft

Let l be the Slant height of cone.

$\therefore \: l = \sqrt{ {h}^{2} + {r}^{2} } \\ = \sqrt{ {3}^{2} + {3}^{2} } \\ = \sqrt{9 + 9} \\ = \sqrt{2 \times 9} \\ \therefore \: l= 3 \sqrt{2} \: ft \\ \\ total \: surface \: area \: of \: cone \\ = \pi \: r(l + r) \\ = 3.14 \times 3(3 \sqrt{2} + 3) \\ = 9.42 \times 3( \sqrt{2} + 1) \\ = 28.26 \times (1.414 + 1) \\ = 28.26 \times 2.414 \\ = 68.21964 \\ \approx \: 68.2 \: {ft}^{2}$