Question

Find the slant height of the cone with the given measurements, rounded to the nearest hundredth. Then use your result to find the surface area of the cone. Use 3.14 for π. Round the final answer to the nearest hundredth.

height: 10 yards
diameter: 16 yards

Question 20 options:

522.75 yards2

321.79 yards2

102.48 yards2

1751.87 yards2

Answer 1

Check the picture below.

`\bf \textit{slant height of a cone}\\\\ SH = √(h^2+r^2)\qquad \implies SH=√(10^2+8^2)\implies SH=√(100+64) \\\\\\ SH = √(164)\implies SH\approx 12.80625\implies \stackrel{\textit{rounded up}}{SH = 12.81} \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cone}\\\\ SA = \pi r√(h^2+r^2)+\pi r^2\implies SA=\pi r\cdot SH+\pi r^2 \\\\\\ \stackrel{\textit{using }\pi =3.14}{SA = (3.14)(8)(12.81)+(3.14)(8)^2}\implies SA = 522.7472\implies \stackrel{\textit{rounded up}}{SA = 522.75}`

Answer 2

Answer:522.75 yards2

Explanation:

The diagram of the cone is shown in the attached photo. The slant height forms the hypotenuse of the right angle triangle formed. The radius of the base of the cone is

Diameter /2 = 16/2 = 8 yards

To determine the slant height, we would apply Pythagoras theorem which is expressed as

Hypotenuse^2 = opposite ^2 + adjacent ^2

Slant height^2 = 8^2 + 10^2 = 164

Slant height = √164 = 12.81 yards

Formula for Total surface area of a cone is expressed as

πr^2 + πrl

L represents the slant height

π = 3.14

Therefore, total surface area

= (3.14 × 8 × 8) + (3.14 × 8 × 12.81)

= 200.96 + 321.7872

= 522.75 yards